THE MICHIGAN STATE UNIVERSITY IRON-FREE DOUBLE FOCU‘SING BETA-RAY 'SPECTROMETER Thesis fox She Degree of Ph. D. MICHIGAN STATE UNIVERSITY Libor Jiri Velinsky I964 MINI!“ WWII?MININHHHHNIII 01743 0038 [ /” ‘ m -. ~15 "- -AQ: .4‘ ABSTRACT THE MICHIGAN STATE UNIVERSITY IRON-FREE DOUBLE FOCUSING BETA-RAY SPECTROMETER by Libor Jiri Velinsky A 30 centimeter radius iron-free ’EIVE'beta-ray spectrometer using the Moussa focusing coil configuration and some features of the Vanderbilt University instrument, was designed and constructed. The design, construction and testing of the machine are discussed in detail. With 6 5 stable environment a 32:10 short range and a 15:10 long range stability was achieved. To test the performance of the instrument, the in- 137m was examined with ternal conversion spectrum of Ba 0.047% resolution. The relative line intensities obtained were: K: LI: LII: LIII: MI: MII,III: MIV,V a (13.04): c.1401.007):(.02071.0046):(.01711.0041):(.02333.0030): (.01451.0020):(.00471.0016). The x and L shell results are in agreement with those of Geiger et al. The M shell results are new. 210 was ob- The internal conversion spectrum of Bi tained with 0.18% resolution. The relative line intensi- ties are: LI: LII: LIII: M1: M11: MIII: NI: NII: NIII: * - I - I - I "Iv-VII+OI+PI . (1-.034).(.1l1 .007).(.0094 .0028).(.229 .007):(.023i.003):(.00291.0022):(.05971.0038):<.00691.0011): (.00123.0005):(.0151.003). The intensity ratios in the L Libor Jiri Velinsky shell and the MI/MII ratio agree with theory for pure M-l radiation. In both experiments the M shell line intensi- ties fall considerably below Rose's calculated values. The discrepancies are consistent and agree with measure- ments of Backstrom et al., for H9199. THE MICHIGAN STATE UNIVERSITY IRON-FREE DOUBLE FOCUSING BETA-RAY SPECTROMBTER BY Libor Jiri Velinsky A THESIS Submitted.to -Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1964 ' ACKNOWLEDGMENT It is a pleasure to acknowledge my indebtedness to Professor Sherwood K. Haynes, whose direction, encour- agement and patience were invaluable throughout the course of this work. I wish to thank him particularly for allow- ing me to take a lion's share of the decision-making re- sponsibilities during the design of the spectrometer, for it transformed a straightforward construction project into a creative learning experience. The intimate encounter with the myriad of details involved in this work was in- valuable to me. I am grateful to the members of the staff of the Department of Physics for their help and encouragement and to Mr. R. J. Krisciokaitis for many useful discussions and his assistance, particularly during the stability tests and the data collection runs. I am indebted to the late Mr. Charles Kingston for his help and his many suggestions pertaining to the mechan- ical construction of the spectrometer. My thanks also go to N. R. Mercer, R. B. Hoskins, R. w. Cochrane, D. Salemka. and N. Rutter, the staff of the machine shop, and to E. F. Brandt and w. Harder, Jr., of the electronics shop, for their part in the construction of the spectrometer. Last but not least, I wish to express my thanks to my wife Marilyn, whose assistance, encouragement and support were invaluable to me. I dedicate this work to her. The spectrometer was constructed and operated with the aid of a financial grant from the National Science Foundation. 11 ACKNOWLEDGMENT. LIST OF TABLES. LIST OF FIGURES INTRODUCTION. . TABLE OF CONTENTS CHAPTER 1. SURVEY OF BETA-RAY SPECTROMETERS. . . . . CHAPTER 2. ELECTRON OPTICAL PROPERTIES OF AXIALLY SYMMETRIC MAGNETIC FIELDS . . . . . . . . 2.1 2.2 2.3 CHAPTER 3. IRON 3.1 3.2 Basic Definitions and Relationships. The Equations of Motion and the Series Representation of the Magnetic Field Focusing Properties of Axially Symmetric Magnetic Fields. . . . . . FREE DOUBLE FOCUSING SPECTROMETERS . Focusing Coil Configurations . . . . Determination of Focusing Coil Parameters . . . . . . . . . . . . . CHAPTER 4. CONSTRUCTION OF THE SPECTROMETER. . . . . 4.1 4.2 Introduction . . . . . . . . . . . . Construction of the Focusing Coils . (a) The Coil Mounts (b) The Winding Procedure (c) The Coil Terminals and Leads The Vacuum Chamber . . . . . . . . . The Source End Assembly. . . . . . . The Counter System . . . . . . . . . (a) Introduction (b) The Side Window G.-M. Counter (c) The Counter Gas Flow System (d) The Data Acquisition System The Baffle System. . . . . . . . . . iii Page ii vi vii 13 13 17 26 37 37 41 48 4B 51 6O 64 67 77 CHAPTER 5. CHAPTER 6. CHAPTER 7. 4.7 The Focusing Coil Temperature Control System . . . . . . . . . . . (a) Introduction (b) The Circulating System (c) Thermostatic Control The Vacuum System. . . . . . . . . . (a) The Vacuum Pumps (b) The Vacuum System (c) Electrical Controls and Associ- ated Equipment FOCUSING COIL CURRENT CONTROL SYSTEM. . . 5.1 5.2 5.3 5.4 Introduction . . . . . . . . . . . . Design and Construction of the Transistorized Power Supply. . . . . (a) The Input Section (D) The Rough Regulator (c) The Fine Regulator Loop (d) The A.C. Feedback Loops (e) Fine Regulator Construction Notes (f) Regulator Operation The Rotating Coil System . . . . . . (a) Introduction (b) The Field Sensing Coils (c) The Rotating Shaft System (i) The rotating shaft, its drive and supports (ii) The rotating shaft con- struction notes (d) The Permanent Magnet Assembly The Performance of the Current Control System . . . . . . . . . . . EXTERNAL FIELD COMPENSATION . . . . . . . 6.1 Introduction . . . . . . . . . . . . 6.2 The Compensating Coils . . . . . . . 6.3 The Compensating Coil Power Supply . 6.4 Performance. . . . . . . . . . . . . ALIGNMENT OF THE SPECTROMETER . . . . . . 7.1 Coil Measurements. . . . . . . . . . 7.2 Computer Runs for the Optimization of the Focusing Field. . . . . . . . iv m w c (D 0) (D 97 97 98 118 148 153 153 154 155 158 163 163 171 CHAPTER 8. CHAPTER 9. CHAPTER 10. REFERENCES. 7.3 Alignment of the Spectrometer. . 7.4 Phasing of the Rotating Coils. . COUNTER WINDOW AND SOURCE PREPARATION 8.1 Counter Window Preparation . . . 8.2 Source Preparation . . . . . . . PERFORMANCE OF THE SPECTROMETER THE CONVERSION ELECTRON SPECTRUM OF CS - Ba 137 o o o o o o o o o o o o o 9.1 Introduction . . . . . . . . . . 9.2 The Conversion Electron Spectrum CS " Ba 1370 o o o o o o o o o o 9.3 The Experiment . . . . . . . . . (a) Source Preparation (b) Data Collection (c) Data Analysis 9.4 Results and Conclusions. . . . . THE CONVERSION ELECTRON SPECTRUM OF RADIW D. . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . 10.2 The Decay of Radium D. . . . . . 10.3 The Conversion Electrons of Radium D 10.4 The Experiment . ... . . . . . . (a) Source Preparation (b) Data Collection (c) Data Analysis 10.5 Results and Conclusions. . . . . 203 203 204 207 211 217 217 220 226 230 242 Table I. II. III. IV. V. VI. VII. VIII. IX. LIST OF TABLES FOCUSing COil Data . . . . . O C O O O O O O O Coil Winding Cross Sections. . . . . . . . . . Equivalent Radii and the Spacing of Current Filaments for the Focusing Coils . . . . . . Axial Spacing of the Focusing Coils. . . . . . The K Conversion Coefficients and the K/ZS L Line Intensity Ratios for Ba137m . . . . . . Relative Conversion Line Intensities . . . . . 137m Conversion. Relative Intensities of the Ba Summary of RaD Conversion Electron Data. . . . Relative Intensities of the RaD Conversion Lines . O . O O O O 0 O O O O O O O O O O O 0 vi Page 56 166 187 206 207 213 231 238 Figure 1. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. LIST OF FIGURES Transmission as a fUnction of the field exffiCient 32 O O O O I O O O O O O O O O O Focusing coil arrangement due to Siegbahn and Edvar son 0 O O O O 0 O O O O O O O O O O O O (a) Focusing coil arrangement due to Moussa (b) Focusing coil arrangement due to Lee- Whiting and Taylor . . . . . . . . . . . Plot of fVVSZ versus 0C . . . . . . . . . . . Overall view of the completed spectrometer . . Cross-sectional view of focusing coil mounts . Schematic diagram of coil winding apparatus. . Schematic representation of the focusing coil power connections. . . . . . . . . . . . . . Spectrometer vacuum chamber. . . . The source end assembly. . . . . . r . . . . . \ The source end assembly (photograph) . . . . . The Side Window G-M counter. o o o o o o o o o (a) (b) Assembled counter Counter positioned on spectrometer plate 0 O 0 O I O I O O O O O O O O I O 0 Counter gate assembly. . . . . . . . . . . . . Counter gas flow system. . . . . . . . . . . . Counter gas flow system panel. . . . . . . . . Beam defining baffles. . . . . . . . . . . . . Spectrometer baffle positions. . . . . . . . . Focusing coil temperature control system . . . Focusing coil temperature control system. The pump and the heat exchangers . . . . . . . . vii Page 34 38 40 44 50 54 S9 61 63 66 68 70 72 74 75 78 80 82 84 86 Figure 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. Focusing coil temperature control system. The control circuit. . . . . . . . . . . . . . . Block diagram of the main vacuum system. . . . High vacuum water cooled baffle. . . . . . . . Vacuum pump control circuit. . . . . . . . . . Block diagram of spectrometer power supply Schematic diagram of the spectrometer power supply 0 O . O I O O C O O O O O O I O O I 0 Schematic diagram of the error signal ampli- fiers and the phase sensitive detector . . . Schematic diagram of the chopper driving CirCUito . O O O O O O O O O O O 0 O O O O 0 Section of the rotating shaft. . . . . . . . . Schematic diagram of a shaft section . . . . . Cross-section of the spectrometer end of the rotating shaft . . . . . . . . . . . . . . . Cross-section of the central driving pulley. . Photograph of the shaft drive. . . . . . . . . Permanent magnet assembly. Mechanical phase contrOI O . O O O O O O 0 O O O O O O O O O 0 Schematic diagram of the compensating coils current regulators . . . . . . . . . . . . . Residual vertical field. . . . . . . . . . . . Decomposition of a rectangular cross—section coil into equivalent current filaments . . . Magnetic field of a circular current. Defini- tion of symbols. . . . . . . . . . . . . . . Radial field of the B coil pair as a function of its displacement relative to the median plane of the spectrometer. . . . . . . . . . Radial field of the C coil pair as a function of its displacement relative to the median plane of the spectrometer. . . . . . . . . . viii Page 89 92 93 95 99 103 109 112 129 131 136 139 142 145 157 159 164 169 173 174 Figure 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. S3. 54. 55. 56. Radial field of the D coil pair as a function of its displacement relative to the median plane of the spectrometer. . . . . . . . . . Radial field Variation in coils) . . Variation in coils) . . Variation in coils) . . Variation in coils) . . Deviation of as a function of radius . . . . . B zas B as 2 total a function of radius (A . . . . . . . . . . . . . O a function of radius (B a function of radius (C a function of radius (D axial field from ideal sixth order field (A coils moved). . . . . . Deviation of total axial field from ideal sixth order field (B coils moved). . . . . . Deviation of total axial field from ideal sixth order field (C coils moved). . . . . . Deviation of total axial field from ideal sixth order field (D coils moved). . . . . . Source evaporator. Internal conversion lines of C5 137 _ Bal37m. Conversion line intensity ratios as a function of transition energy . . . . . . . . . . . . The conversion electron spectrum of RaD. . . . Conversion line of transition Conversion line of transition intensity ratios as a function energy 0 C O O I O O O O O O O intensity ratios as a function energy 0 O O O O O O O O O O . ix Page 175 177 178 179 180 181 186 199 210 212 233 236 237 INTRODUCTION Nuclear physics owes its beginnings to Henri Becquerell and his discovery of the natural radioactivity of uranium compounds. Subsequent interest in this phenomenon led Ruther- ford and Soddy2 to suggest that radioactive disintegrations result in changes of atomic species; Rutherford to identify alpha particles as helium nuclei,3 and from the results of his now famous scattering experiment to propose the nuclear atom.4 Although stable isotOpes were discovered by J. J. 5 Thomson in 1913, it was not until 1932 that the experiments of Curie and Joliot6 led Chadwick to the discovery of the neutron7 and thus the completion of the basic inventory of the nucleus. Two years later, in 1934, experiments of Irene Curie and Joliot8 dealing with the alpha particle bombard- ment of light nuclei, established the existence of artific- ially radioactive isotopes. This period also witnessed the [xoposal of the DeBroglie hypothesis and the next step in the development of the old quantum theory when Erwin Schroedinger formulated the principles of wave mechanics.9 These are but few of the events in the history of umdern physics that were responsible for the birth of nu- clear spectroscopy. Progress in this field was relatively slow until the end of the second World War, when the availability and use of nuclear reactors and high intensity accelerators made possible the wholesale discovery of artificially radioactive nuclides and their production in appreciable amounts. It was also during this period that instrumentation became sophisticated enough to enable us to observe the products of nuclear decay with relatively high precision. Since then, a great deal of attention has been devoted to this area of physics. At the present time the amount of information presented to the inquirer every year is nearly astronomical and the problem of rapid recovery of pertinent information from published material is becoming more acute with every passing year. The purpose of nuclear spectroscopy is the collec- tion, analysis and interpretation of data concerning the positions of the various nuclear energy levels, their quan- tum numbers and characteristics of decay, to yield informa- tion necessary for-testing the host of existing nuclear models and theories describing the various aspects of the decays. Only such experimental observation can form a sound tmsis for justification of theoretical predictions, and only these two, hand in hand, can bring us a closer under- standing of some aspects of the nuclear problem. For most radionuclides, nuclear spectroscopy involves the study of the gamma radiations and the beta emissions from the atom. The study of the beta radiations concerns the identification of the number of beta-ray transitions present, the measurement of their branching ratios and their end-point energies, thereby ascertaining the nuclear energy levels responsible for these transitions. The measurement of the shapes of the beta-ray spectra provides information about the spin and the parity of the levels involved in the decay. The primary concern of gamma ray spectroscopy is the measurement of the energies and the intensities of the various gamma ray transitions present in a given decay and, by use of appropriate experimental techniques, the determi- nation of the quantum numbers of the nuclear levels respon- sible for the decay. Gamma ray spectra can be studied di- rectly by means of scintillation and crystal spectrometers, or indirectly by performing a magnetic momentum analysis of external or internal conversion electrons. The internal conversion electrons trace their ori- gin to a nuclear process. A nucleus decaying from an ex- cited state can emit a gamma ray whose energy corresponds to the energy difference of the nuclear energy levels in- volved in the transition. Alternately this energy can be transferred directly to an orbital electron which is then ejected with a kinetic energy corresponding to the energy of the gamma ray less the binding energy of the electron in its orbit. Internal conversion electrons emitted from the various shells and subshells of the atom thus form mono- energetic groups, the study of which can provide informa- tion about the nature of the nuclear transition. For in- stance, the internal conversion coefficients which are de- fined as the ratio of the transition probability for internal conversion to the probability of gamma ray emission are found to be sensitive to the multipolarity of the compet- ing gamma radiation. In cases where the probability of internal conver- sion is very small, external conversion can be employed where the gamma radiations from the nuclide under study are allowed to fall upon a converter foil and the result- ing photoelectrons are analyzed. External conversion can be used to determine the relative intensities of the vari- ous gamma rays. The internal conversion process, electron shakeoff, and the class of decays called orbital capture, give rise to another process which results in the ejection of mono- energetic electron groups: The Auger effect. Following an orbital capture or internal conversion, the atom is left in an ionized state, or, as is often said, there is a pri- mary vacancy in some particular electronic state. This vacancy is filled by a reorganization of the electron pOpu- lation of the atom either in a radiative manner by the emis- sion of X-rays or optical quanta, or, in analogy to the 1 internal conversion process, the energy is transferred to a more weakly bound electron which is then ejected from the atom with a well defined energy. The study of Auger electrons is of interest, since at the present time the amount of accurate theoretical prediction is still quite 10,11 limited. Some recent observations indicate that Auger electron energies are subject to shifts depending on the chemical composition of the source material.12 So far these shifts have not been investigated in a systematic manner. Although the field of nuclear spectroscopy abounds in a wealth of instruments and techniques, an excellent review of which can be found in Siegbahn's book,13 the beta- ray spectrometer remains one of the basic tools and one of the most versatile; for a wide variety of problems can be studied by the observation and the analysis of the energet- ics of electron spectra. To be useful, in the light of present day requirements, the beta-ray spectrometer must possess several essential characteristics: First, there is a need for high resolution. Fre- quently, many gamma ray transitions are found in the nuclide under observation. The internal conversion process thus yields many groups of monoenergetic electrons, correspond- ing to the many shells and subshells of the atom where the the conversion process can occur. Furthermore, radiation- less transitions that may follow the conversion process give rise to an even larger number of monoenergetic lines of Auger electrons. Often, the great number of such lines in the electron spectrum of a radionuclide causes the lines to be very closely spaced and even to overlap. The inter- pretation and meaningful, unambiguous analysis of such spec- tra can only be made if the resolution of the Spectrometer is good enough to separate the various groups of electrons. Second, much of the work done today is with isotopes of low specific activity. High transmission is therefore desirable to make weak lines observable and to enable the experimenter to collect data with sufficiently good statis- tics in a reasonable amount of time. Third, high precision and reproducibility are needed, as the determination of conversion and Auger coefficients requires precise measurements of the intensities and the intensity ratios of the various conversion and Auger spec- tral lines. Fourth, high absolute accuracy and the minimization of systematic errors are needed if one is to be able to make meaningful comparisons with the results of other workers in the field and with different observational methods. The decision to build a magnetic beta-ray spec- trometer at Michigan State University was made in the light of interest in the subject matter of electron spectroscopy and of the general versatility of the instrument. The reasons for the choice of the particular instrument that was finally constructed need some amplification and will be found in the succeeding chapters. .\} CHAPTER 1 SURVEY OF BETA-RAY SPECTROMETERS The various beta spectrometers now in existence can be classified according to the mode of momentum selec— tion into electrostatic and magnetic field deflection in- struments. The electrostatic machines have, as a rule, quite good transmission but poor resolution. Their energy range is limited by the potential that can be applied to the deflection elements without electrical breakdown. At- tainment of very high precision is also difficult since the deflecting electric field has to be kept always pre- cisely normal to the trajectory of the electrons, or if it is not precisely normal, then the amount of acceleration applied to the electron beam has to be well known and under control. Because of these limitations we shall not consider this type of instrument further. 3 The beta spectrometers utilizing a magnetic field for momentum analysis can be divided into two main groups, depending on the direction of the applied field relative to the paths of the electrons. In the lens, or helical type of beta spectrometer the net electron motion is paral- lel to an axially symmetric magnetic field, whereas in the flat, or transverse spectrometers the paths are mainly per- pendicular to the applied field. A further distinction is made among these into iron containing machines and the iron-free machines. Spectrometers utilizing iron or other ferromagnetic material for shaping their magnetic field appear, at first, to be quite attractive. They are economical in use, for the desired magnetic field can be produced with far less current than in the case of an iron-free spectrometer. Further, the large inductance of the magnet coils is a de- cided help in stabilizing the field. Fine corrections to the shape of the field can be made relatively easily by neans of shims or grinding of the pole faces. Thus once the relatively complex calculations for magnet gap shape are accomplished the actual construction of an iron yoke spectrometer might be expected to be simpler than the con- struction of its iron-free counterpart. These instruments have, however, some very serious drawbacks which effectively eliminate them from consideration for low energy, high reso- lution and high precision work: First, it is difficult to obtain field of precisely axial symmetry, having the proper shape over the entire region of electron trajectories, due to the non—removable inhomogeneities of the iron yoke. Such local variations in the field intensity cause perturbations of the orbits resulting in broadening of the image at the focus. Second, hysteresis, the nonlinear relationship be- tween the magnet current and the field intensity, requires precise calibration of the magnet over the entire current range. As the fields generally used for beta spectroscopy are below 1000 gauss and in the case of double focusing spectrometers are highly nonuniform, proton magnetic res— onance cannot be used for such measurements and Hall effect devices lack sensitivity at low fields. Rotating coil sys- tems which are used with most of the high precision iron spectrometers have a precision limit of about one part in 104. This limit is imposed principally by the magnetic properties of the iron yoke. Third, the residual remanence of the iron prevents these machines to be used at very low energies, unless a very careful demagnetization procedure is used. Even so, the precision obtainable in this region is rather low. For these reasons, the iron containing spectrometers will also be dismissed from further consideration. The final choice is to be made therefore among the iron free instruments. The helical spectrometers fall basically into two categories: The short lens, in which the magnetic field is nonuniform and the source and detector are located out- side the field, and the long lens, where the field is more cm less uniform and the source and detector are immersed in the field. Both types of spectrometer were developed to a high degree of sophistication after the second World war. One of the most recent and also the best example of a long 14 lens spectrometer is described by Jungerman et al. He reports 0.018% resolution at 0.04% transmission. In spite 10 of these excellent figures it must be realized, however, that although these machines can be designed to perform close to their theoretical limit and have a very good fig- ure of merit, they do possess several disadvantages for high resolution work at very low energies. The particularly objectionable features are: First, all lens spectrometers are extremely sensi- tive to deviations of the focusing field from cylindrical symmetry. This means that the machining work and the coil manufacture on one of these instruments must be of very high order of precision, and hence expensive. Second, for very high resolution these instruments require a point source, whereas the transverse spectrometers require a line source. Thus the lens spectrometers have eliminated one dimension from the source and therefore the usable intensity for high resolution work will be low. Third, in these machines the line of maximum con- vergence of the electron beam, the so-called "ring focus," occurs some distance from the detector. Typically this distance is one-quarter to one-half of the length of the machine. This means that at the detector the beam is di— vergent and if a maximum of the beam is to be collected the detector must be of large dimensions. This immediately creates the problem of increased background counting rate. Fourth, examination of the equations governing reso- lution in lens spectrometers13 shows that the best resolu— tion is obtained for large angles of divergence of the beam. 11 This means that the detector is looking at particles that are entering it at an included cone of 90° or more. Such high angle of incidence raises serious problems of detec- tion of low energy electrons. If, for example, a Geiger counter is used for detection it will have to be a large end-window affair with a very thin window. A typical win— dow thickness to be expected in this work is a few micro- grams per square centimeter. To contain the gas pressure in the counter, the window must be supported by some means such as a grid, which may cut down the transmission of the window by some 30 to 50 percent even for normal incidence. At large angles, the transmission may be only a few percent. Due to these rather serious shortcomings, particu- larly at the very low electron energies, the lens spec- trometers were also eliminated from further consideration. Another variety of beta spectrometer which does not fall exactly into either of the two main classifications is the ”orange peel" spectrometer. Essentially it is a three dimensional generalization of the wedge sector field Charged particle analyzer found commonly in accelerator laboratories and used as steering magnets. A highly engin- eered iron free representative of this class is the toroidal 596ctrometer of Freedman et a1.15 located at the Argonne National Laboratory. This instrument is capable of very high transmission and good resolution. Freedman reports the following characteristics: 12 Source Diameter Transmission(%) Resolution(%) 1/8” 19 0.93 1/8" 16 0.40 1/8" 2.8 0.21 1/4" 16 0.56 3/8" 18 0.88 1mm 13 0.30 1mm 1.6 0.13 The instrument consists of two toroidal sections that can be used either for beta-beta coincidence measurements, or can be arranged in series to give an instrument with higher resolution at a slight loss of transmission. Aside from the very high cost of such an instrument, due to the extreme precision needed in its manufacture it is not particularly suited for low energy work. It suffers from some of the same objections leveled against the sole- noidal spectrometers, in particular, a high angle of inci- dence of the electron beam at the detector. None of the spectrometers discussed in this chapter thus far seem to be particularly suitable as judged by the criteria put forth in the Introduction. The remaining type, the iron free transverse spectrometer, offers us the last chance, so to speak, and it does turn out to be the best one. Before we can specify the particular kind of trans- verse spectrometer that offers the optimum compromise of all the desirable characteristics for low energy work, we nmst first describe the focusing action of the magnetic field. CHAPTER 2 ELECTRON OPTICAL PROPERTIES OF AXIALLY SYMMETRIC MAGNETIC FIELDS 2.1 Basic Definitions and Relationships The basic relations of most frequent use in beta spectroscopy can be defined as follows: An electron moving with a velocity v through a unifggm magnetic field B oriented perpendicular to its trajectory will describe a circular path of radius of curvature r. Its equation of motion is 8611' : mr'v (1) where m is the relativistic mass of the electron nn (2) 0 a (j- N/Cz)‘/z The momentum of the electron is given by YTI : (3) P=m’U' =e’Bf‘ In these equations e represents the electronic charge. In iron free spectrometers the value of B is a well known linear function of the focusing coil current and there- fore it is convenient to classify electrons according to their momentum in terms of their Br value. 13 14 The resolution_§_of an electron line is defined as the relative width at half maximum of the line. In terms of momentum (4) __AP ABr R- P For a magnetic spectrometer with fixed geometry R is a con- stant. The kinetic energy of the electrons whose momentum is Br can be obtained by use of the relativistic expression for energy: 2 2 z 4 ET : PQC 1" moc (5) I where 8T is the total energy of the electron. Combining equations (5) and (3) we obtain I 2 2 z E = [(moc) + 62c?” (Br) 1/2 (6) 'T The kinetic energy of the electron is BK a BT - moc2 or 2. ' 2. EK=[. (mocz) + (262' (Br)Z]/Z—moc (7) - 2 ‘ ‘_ 2 z 2 z. I /L __' ] EK " mac [ ( mica. B Y- + > (8) This expression is useful for obtaining the kinetic energy of electrons of a given Br value. If the values of the 15 constants are substituted into equation (8), using m0 = 510.984 3 0.016 Kev the kinetic energy in kilo-electron volts becomes EIL: (5.0.954: o-OI6)U(54+2.21 ammo-'08??? 4] (9) Note that equation (8) can be written in terms of relativistic energy units as E = ( PL+|)'/2 -| xii-11.14410) '1 7; ) I“) "_ I Differentiating this expression gives us a simple equation “F\ for energy resolution ,_ —V .tfi cu: =(P + \> L Pap -: QLE _.___ P2 3L8 (11) A good rule of thumb for the resolution in semi- circular spectrometers is R = u”/D (12) "here w is the width of the source and D is the diameter °f the spectrometer's mean electron orbit. EEEBEEEEEAEEF Electrons ejected from a source are e“II-tited in all directions. The defining slits and other baffles in a beta spectrometer will allow only a certain 16 fraction of them to come through to the detector. The ac- ceptance solid angle of the spectrometer is usually expressed as a fraction of the total sphere and is called the geomet- rical transmission, or the gathering power of the instrument. When the spectrometer is set to observe a given monoenergetic electron line it should be noted that all of the electrons emitted into its acceptance angle may not reach the detector, depending on the adjustment of the de- tector slit. Transmission T is defined as the fraction of all of the monoenergetic electrons leaving the source that are actually counted by the detector. T is usually expressed as percent of the total sphere. Luminosity and the Figure of Merit: The luminosity of a spectrometer is defined as L=TS (13) where T is the transmission and s is the area of the source. Th3 ratio of luminosity to resolution is a measure of the performance of the spectrometer and is called the figure of merit. Clearly, this ratio should be as large as pos- sible over the entire momentum range of the instrument. 'Comparison of the various types of spectrometers showsl3’14’16 that the figure of merit can be much higher for transverse spectrometers than for helical machines. Dispersion: Dispersion is defined as the change of the position of the image at the detector for a given change in the Br value of the electron beam. 17 D .. (figs) ”4’ This quantity is intimately connected with resolution of the spectrometer. The equation shows that an increase in the dispersion while the dimensions of the spectrometer are held fixed, allows us to use wider sources with the resolution remaining constant. It should be pointed out that the requirements of high resolution and high transmission are really not mutu- ally compatible, as all electron optical systems suffer from aberrations. Therefore the design of a spectrometer is essentially a search for the best compromise among the desirable properties and the minimization of the optical aberrations. 2.2 The E ations of Motion and the Series Representation of Efie MagnetIc Field The focusing properties of magnetic fields having axial symmetry have been studied in detail by several authors. Svartholm and Siegbahn developed the appropriate equations for the design of a double focusing spectrometer in 1946.17 Later that year Svartholm published a paper concerning the aberrations of such focusing fields.18 In 1947, Shull and 19 developed the same equations employing a some- Dennison what different approach, and attempted to calculate condi- tions favorable for higher than second order focusing. Quite recently, Lee-Whiting and Taylor tackled the problem in a very thorough manner, in preparation for the construction 18 of the one meter radius beta spectrometer located in Chalk River, Canada.20 In the following review, an attempt has been made to integrate the material presented in the quoted articles, and show the development of the various equations of motion from first principles. In the process, the quoted refer- ences were used freely. The notation used is something of a mixture, but is nearest the notation used by Lee-Whiting and Taylor. Indeed, toward the end of this section the Lee-Whiting and Taylor notation was deliberately chosen t6 enable the interested reader to peruse the original ma- terial with a minimum of difficulty. Consider a magnetic field, rotationally symmetric about the z axis and having the x-y plane (at z . 0) as the plane of symmetry. A circular orbit in the symmetry plane and concentric with the z axis will be called a cen— tral orbit or the optic circle. Consider a charged particle in such a field. The most appropriate coordinates for this problem are the cylindrical coordinates, r,(P, z. The mag— netic field is a function of r and 2, independent of 4): the Lorentz force equation is * * _p- here e is the electronic charge, as before and '3' is the Velocity: 19 2, ° 02, ‘2, m 2 (“402+ r +-z up The magnetic field is definable in terms of a vector poten- tial as —b- —a- ->- B =VxA with the auxiliary condition V.A =0 (18) Clearly, only the 4) component of TA» will be nonzero. This component will be denoted simply by A. Equation (18) now assumes the explicit form Br(r,:z,) z: — g—AE- (19) 9 VA) Bz(nz)=-% 3v mm Combination of equations (16), (l7), (l9) and (20) gives the time dependent equations of motion of the particle J. ' .. '9- 'ErA) < ) 4.0““) ‘mw +9439? 21 0L ' .. '16.. .L 2' _ _ ‘ __A. _ '.._..3<*A) ~dt(mrct>)— erzm Zr Dr (23) Integral of equation (23) is a constant of motion, the com- ponent of momentum corresponding to the coordinate 4>: A. z. - 0L <) 3(mr4>+er)eoe—Eu 24 or (I) = u _ elf-A (25) mr The equations of motion can now be rewritten in the form: 00 a ‘ u 2 r = —— ——k——-—-z ) I m 3. 2m v. A (26) mi: ~i{_L44-—cAf] he) 92 2m r These equations are identical with Svartholm and Siegbahn l7 equations 6 and 7. In preparation to transformation of the equations of motion into dimensionless form, let us first change the independent variable from time to the angle (3, since ultimately we are more interested in the path of the electron as a function of the angle rather than time. To condense the equations further, define U=U(r.1)= it“? ’ZA)Z (27) treating u as a constant. Then ‘/ u l I 9 (28) r + —.- Y- = -- . ¢ M¢13V ., 1 l 2' A; ,2) = _ |.2 D (28) mm 3'2 quferentiation with respect to (p is denoted by primes. Transformation into dimensionless form is accomplished by “Sing the parameters «'4'. 2 where ro is the radius of the mean orbit. 21 We need an explicit expression for 4). Note that equations ' ,_ I (25) and (27) give —— Tn? ,Izm'u and that for an elec- tron traveling on the mean orbit, r s ro and z a 0, we shall have stationary motion if the relation p. is satisfied. (30) 2 r6 82mm = - For such an orbit we can write (to: vo/ro and hence . =—WT‘-;_- i/Zmu = 409(3.§) <31) where the new function C}(d}§) is defined as 6mg) 2 mi». 2m’li (32) The relation (29), (30) and (31) combine to give the dimen- sionless equations of motion cS"+[G‘ 35%, 5 + ‘EL'I'DG :5 SIJI=] {Ody-5 95%- +I+J] (33) L C; §”+[—é%—g§6 +— ggélékl =' (”5) J; 953‘ (331) These are identical with equations 16 of Svartholm.18 As the focusing field enters these equations through the function G and in particular, the product rA, the solu- tion must be approached by expressing G explicitly in terms of 5 , g , and 80' The order of the calculation is then determined by the number of terms that are retained in the eexpansion of G. Furthermore, since we are not interested i“trajectories coincident with the mean orbit, we must allow the electron a variation in the initial momentum, t [1.1 ‘l‘l'l‘ III‘II‘I‘I‘I' 22 position and angle subtended with the tangent to the mean orbit. A set of such initial conditions imposed on the electron at its starting position 4): 0 can be written as p=f>.(l+e) <34) 6°: h ’ 30: t (35) , as '_ .213. _. 5° -“-' (3;), = H 3 (o- (34,): T (36) Note that the velocity vector of a particle traveling paral- lel to a tangent to the mean orbit is A. —.. . N. = I r.(8+t) 41¢ and the velocity vector for a particle which deviates from the tangent by having radial and axial components of veloc- ity nonzero is J .6, A . [A . A N = (64> )r +(G¢§)z+[fis(5+i)4)]¢ The angle between these vectors is given by —a- -—-r- UQIoWT (:03 = T mum or explicitly in terms of the initial values 1 2 "V1 cos = I+ H +T (37) T (1+k)‘ Recalling the expressions for G, U and u: G(8,§)= mi?“ j/Zm’u u -— -‘— (es—2A? ”u, = mrchJ +ZVA 23 note that for stationary motion on the mean orbit u has the value 1). = mam. +qu. (38) This expression is modified by introducing the initial con- ditions so that r. ——- (I + h) r. Va 9 {U}, COS’3A The function u then has the form =~"("*€)(l+ Mcosa‘ (man) + Uvo (39) and the function G assumes the explicit form C(5f)= (I+ ‘az{(l+e)(l+h)cosx +mv———;,°~r(A —rA)} (40) In this equation rA can be expanded in the neighborhood cfi’the mean orbit. The resulting series is used in conjunc- tion with the equations of motion (33) to obtain the desired solutions of (S and g as a function of (I) . Lee-Whiting mulTaylorzo have performed such calculations and have car- ried them numerically up to the sixth order. Since their treatment is not only the most recent and thorough, but also mathematically the most elegant, we shall sketch its Inainfeatures here: It is convenient to define another function, F, and express it in terms of G: F(5,§) = (\+5)" G(5,§) (41) 24 The equations of motion (33) are therefore also modified. The new equations are I | ’4 6+{%§-§3+—é—%§§-0E5)6H}5 =~(|+6) —L——§— -'-:(I+S) (42) W ll 3‘: I LEE I 3F- 1 “HT-6+ F £5 (my) 8}§'H"“*5) FS’ (42) The product rA is now expanded in the neighborhood of the mean orbit as °° Ht n. FA=QA.-m%g'EZCmn§ 5 (43) ngnzo In this expansion note that not all coefficients are per- mitted to have nonzero values. The field that we assumed at the beginning of this section has a plane of symmetry at z . 0. Therefore also 5' a 0 there. This makes all odd m coefficients equal to zero. Furthermore on the mean orbit rA a rvo. Thus Coo - 0. Equation (30) requires that C01 2 1. Introduction of the particle's initial con- ditions results in VA" foo-A mU.___f; Z Cmn {gm sn_ tmkn} (44) mn=o and the function F now assumes the form F(8,§)=(|+€)(I+h)cos?{‘ +X— Cmu{3m5n-tm 11“} (4S) m,n=o The equations of motion are then solved using this equation. Before further calculations can be done we must 25 establish relationships among the C coefficients. To do this we shall require that Maxwell's equations be satisfied. Thus QB:- _ as, 35 " g 5 (46) I QCVAJ Now using equations (19) Br=—%A£— and (20) Bz=_r_ 8V and equation (43), we express (46) in terms of the expan- "1 n sion and equate the coefficients of _§ 5’ . The result- ing equations (m +2XMH) {C(m+2)(n+l)+ C(mZM} =4“ I! 2.){(m 3) Chub”)+ h awn} (47) Fbr' NEBOu (m+2)(m+l) C(m+2.)o = 4.sz + CW (48) are the Lee-Whiting and Taylor equations 12 and 13. The coefficients Con are independent and if they are specified, all others can be obtained from the above recurrence rela- tions. The focusing field B, in the plane of symmetry (2 - 0) and in the neighborhood of the mean orbit, can be ‘ expressed in terms of a Taylor series expansion B nso Where the coefficient a0 = l, and the an are given by 2b n n 0h :: -_E_ (d B“) (50) n! BUB) d r r, The relationship between the an and the Con is found from equations (20) and (49) a, \ QLrA) " B("'°)""F er = EWING): ““5 or explicitly “=° zoo n "4 0° “ ( ) I BUN“ Z: TConS :' 80202.: ans 51 SQ“) on=o o “=0 Again, equating coefficients of equal powers gives the re- currence relationship _. (52) “Con _ an‘l + ah-Z. This expression is valid for r\:?‘ , provided that we define a_1 - O. 2.3 Focusing Properties of Axially Symmetric Magnetic Fields Consider the first order solutions to a field hav- ing the form B(Y‘,O) : BUCHO) {I + ans } (53) Substitution of the explicit form of the function F into the equations of motion (42) gives, to first order 6 + ZCOZJ=6 (54) I §' 4' .Z.(Lzo % ==(3 (541) 27 The solutions of these equations are 8: EEC—:1 5‘."- IZC01 (P + h. COSJZCOI 4) + +2€C°z{|—COSfiZ_o-ZC‘DB (55) f = (5%; 5;“V2Cu 43 + tcos {zczo 4; (551) The initial conditions (34), (3S) and (36) are included in the above equations. These solutions are somewhat more general than the results given by Svartholm and Siegbahn, who assumed that the electron starts from a point on the mean orbit with momentum p0. If we restrict ourselves to such initial con- ditions, then h = t = O and e; a 0. Equations (55) reduce to 8’ (2:6; SinJZC-O‘L 4’ (56) 'T‘ . f: [F20 S'WZCzo ‘t’ (561) Clearly, at the source 4> = 0 and the initial coordinates of the electron are¢S == h a 0, g a t a 0; as we said be- fore. The electron beam is focused at an angle when (S and g are again equal to zero. That is VZCoz. 4) =' VZCu, (b = kw (57) We shall consider only the first focal point and let k = l. The radial and axial focusing angles are 28 _, 7C IVS — HE: (58) w§ '3 L (581) 12 C20 The recurrence relation for the C coefficients, equation (48) gives __ l . C02, "‘ C20 - 1" Since col = l. (59) Combining (58) and (S9): I I 2(C°1+C2°) I (so) + —; = = -— 1P“ ‘I’; It" W" Which is the Svartholm and Siegbahn equation. A special case of this is the uniform magnetic field sPectrometer. There B(r,0) a B(ro,0), the radial focusing al'lgle is 7? , and 7C _ IVS-'1“ '3')? hence Coz=:‘z_, and Clo—O 12C“ Therefore 1"; is indeterminate and no axial focusing takes Place. To obtain the dispersion in this case, consider the radial displacement of the image for an electron of initial momentum p -- po(l + e ). This means that we use s0<>lution (55) with h a 0: now set 4325?, 5: (:3 = H 5("4’ + e(I— cost) 29 The radial displacement is c42==zén mu . Conditions for first order double focusing are found kw’solving equations (57) and (58) explicitly. Then C02 = C20,: 1/4, and the focusing angles are 1P3 =1)“ = VIZ (62) In analogy to (47) we have for this case V-C; =4éfi; (63) For double focusing the dispersion is therefore doubled. The value of the field coefficient a is found from 1 the recurrence relation (52) 2C +8 02 al 0 58 a0 a 1, a1 . - 1/2. The field form for first order double 1’Oczus ing is therefore B(r,0) - B(ro,0) <1 - 1/2 5' ). (54> The solutions (56) written for the double focusing cfise SzHrz sin-ézf and §=TE$‘“% ~ 8 := __. how that S and 5 have maximum values for (i) \IZ . inhese are approximately the maximum deviations of the par- ticles from the mean orbit. We have a way, therefore, to find the transmission by considering the projections of 30 the particle momentum —p’ on the z = 0 plane and the plane defined by ‘15; and a line parallel to the z axis. Taking the tangents of the angles that these projections subtend with Y); we have r.:)>5' ()1 tan Tr: (65) (42). tanxz~ -——-=f (551) and using the initial conditions, I I 5 = H ) S = T the transmission, in terms of a fraction of the total sphere, is 2. erax ' 2— X!- max me . TM“" (66) t: 4% = T In the case of uniform field this expression is modified due to the absence of axial focusing. Same considerations as above give the same value for radial angle: tan Yr =5; H. The axial angle must be limited, however, either by the Spectrometer chamber height or by the height of the detector Slit. The transmission is therefore ZYrmax - 2. 3‘!- detector 4")? and a comparison of the two cases shows Tunfiorm Held '5‘ Ldouble Foc. = X2 max ) rid¢t { I - i‘5 + =38 *0-2995 + 6 + 0.2454 - o-zoz. 55 + 04775 +-~} (73) In conclusion, it is clear that to realize a double focusing instrument with small aberrations and no undue hardships of manufacture, we should strive for an accurate fit to the second order field shape with a1 = - 1/2 and 32 a 3/8, and approximate the higher order field near the nean orbit by suitable positioning of the field producing Currents. This assumes, of course, that sufficient funds are not available to manufacture a set of focusing coils to the standard of precision necessary for fitting the higher order field. The adjustment method seems to have worked quite well in the case of the Michigan State University Spectrometer. CHAPTER 3 IRON-FREE DOUBLE FOCUSING SPECTROMETERS 3.1 Focusing;§oil Configurations The demonstrated superiority of‘the iron-free in- struments over the iron-containing machines for high pre- cision and high resolution work has resulted in a great amount of interest in them and many are to be found in all corners of the world. In view of the large amount of de- Sign effort invested in these instruments since their in- vention in the nineteen forties we would expect a variety 0f ways employed in producing the desired shape of the fo- cusing magnetic field. This is not the case. At this time there are basically two methods for shaping the focusing field of the type described in the last chapter. The first nethod was developed by Siegbahn and Edvarson.21 It con- sists of two coaxial solenoids in the shape of tight cir- cular cylinders. A schematic cross-section of this type 0f coil is given in Figure 2. These so—called "Siegbahn" type spectrometers have been built by Siegbahn and Edvarson in Sweden, by Wapstra and DeVries in Holland,22 by Mladjenovic in Yugoslavia23 and by Hollander et al.24 in this country at Berkeley . Although attractive from mechanical viewpoint for inheir simplicity, these instruments have some drawbacks. 37 38 SYMMETRY AXHB I I 0Rarr I SYMMETRY O - - . .- PLANE I l FIGURE 2. Focusme con. ARRANGEMENT DUE TO SIEGBAHN AND EDVARSON . 39 One of these is the difficulty of realizing the proper field shape for matching field coefficients higher than the sec- ond order. To solve this problem, most likely, the density of coil turns would have to be made a function of z and would have to be accurately computed beforehand, as adjustments on a finished instrument are all but impossible. The co- axial solenoid design also limits the radial departure of the electrons from the mean orbit and due to the positions of the coils; these machines have a very restricted acces- sibility to the source and the counter. The second method of obtaining the prOper field shape uses several pairs of symmetric thin coils. Two main designs are currently in use, one due to Moussa and Belli- card,25’26 and the other due to Lee-Whiting and Taylor.27 Their respective coil configurations are shown in Figure 3. Both schemes use four pairs of coils. There is in essence no difference between these two in terms of their ability to produce focusing fields matched to orders higher than the second. The advantage will lie with the instrument of larger mean orbit radius and the higher degree of engin- eering and general precision of construction that is invested 28 does have a slight edge on in it. The Canadian design the Moussa design in that it is more accessible and that the coil configuration yields a zero total field at the origin of the spectrometer's coordinate system thus allow- ing the use of photomultipliers for coincidence studies. A spectrometer patterned along the design of Moussa 4O AXIS E J E M ORBIT SYMMETRY _._-_°_-__-—° - PLANE E —I- a a (A) _ _ -0 - - + - -O-SYMM§TRY :ILIZ-En PM“ LE ' M FIGURE 3. (A) FocusING con. ARRANGEMENT DUE TD MDUSSA. (B) FOCUSING con. ARRANGEMENT DUE TD LEE—WHITING' AND TAYLOR. 41 was built at Vanderbilt University by Haynes et al.29 This instrument was constructed before the Canadian design was finished. It differs from the Moussa spectrometer in hav- ing a larger mean radius, 300 millimeters as compared with 210 millimeters of the Moussa machine, operates with low voltage-high current coils and uses field rather than cur- rent regulation. The spectrometer constructed at Michigan State Uni- versity was originally intended to be a direct copy of the vanderbilt machine; however, profiting from experience gained with the Vanderbilt spectrometer, it was possible to manu- facture a more precise set of focusing coils, thus enabling the Michigan instrument to have better Optical properties. Furthermore, the author has at times disregarded the Vander- bilt design altogether, in favor of new and hopefully, better one. Thus, although the basic dimensions of the two instru- ments are the same, there are many differences between them that justify a complete description. 3.2 Determination of FocusingyCoil Parameters The determination of focusing coil radii and dis- tances from the z . 0 plane can be carried out by detailed computer-assisted calculations fitting the sixth order ideal field, as was done by the Canadian Chalk River group,28 or by a somewhat more empirical approach following a scheme 25 Since our spectrometer worked out by Moussa and Bellicard. was patterned originally after the French design, its basic focusing coil dimensions were calculated using the Moussa 42 and Bellicard method. The following few pages show the basic steps involved in this calculation. Moussa and Bellicard fitted a field having the shape (74) 3030) = B (rob) gt)” This shape gives a fairly good approximation to an optimum focusing field, even to the sixth order, provided that the radial deviations from the mean orbit are small. The method consists of calculation of the field due to a chosen number cu circular current filaments spaced symmetrically about the median plane and the comparison of this field with the desired one. The parameters of the current filaments (radii and axial positions) are adjusted in progressively finer steps until the desired degree of fit is reached. A brief outline of this method is presented below: Consider a circular filament of radius R, spaced a distance 2 from the plane of symmetry at z . 0. We can de— fine dimensionless parameters 0( and [3 such that r . 2 (75) 0(=‘—_ ) “=— R _ fl R. The axial field produced by such a filament at a point any- where except on the filament itself can be written as an expression involving elliptic integrals of the first and second kind B = P"; I I“ 0‘2 “’52 2- ZIRwawm (.-o()’-+/s’~ E + K (76) 43 The derivation of this expression will be found in Chapter VII. The modulus of the elliptic integrals E and K is I212, = 4“ (77) (I +4)?" +[52’ The field can be therefore schematically expressed as 8, =m F(°<./5) (78’ The function f ( O( , /3 ) can be tabulated for chosen ranges of o( and [3) , i.e., the radial and axial range of departure of the electrons from the mean orbit. Moussa gives a table ofvalues offfor O$O(5"5 3 °$p£ I1 Since in this case the field to be fitted is )1/2 ca Bz.(r)]'/2 a Constant, the product f( o( , (5 ).( o( n be plotted against o( , using {5 as a parameter to obtain a family of curves, as shown in Figure 4. The Bz r a constant field will be matched even for a single pair of coils at a point of zero slope on these curves. The pres- ence of sizeable curvature of these curves shows that spec- trometer constructed in this way would permit only a very narrow radial departure from the mean orbit. To obtain a good fit over an extended region of space, more coil pairs are needed. The choice of the i and(3 parameters is made as follows: Points on the vari- ous curves are chosen in regions of minimum curvature and at points where the slopes will sum to zero. This will 44 ~4— .. ...-__‘L_.—_. "-4.— ID 0L. FJEC VERsus at. P LOT OF FIGURE 4. 45 clearly require that an even number of coil pairs is chosen. Ideally, the curvatures for the various coil pairs should also cancel. This procedure permits an infinity of possible solutions. The number can be reduced by placing constraints on the values of R and z. The coils must not encroach on the electron orbits and they should not be so far away from the mean orbit that an exorbitant amount of power is required to produce a given focusing field. Since the Br value as given by equation (4) is n1 4 f( o( , (5 ), the number of ampere turns needed for a given Br varies as I «1 Roms) This expression shows that while curves with large values of G have small curvature and seem to be the logical choice for coil parameters, they may in fact be unsatisfactory, due to low values of f(°( ,{3 ) and consequently, high power consumption. Bellicard and Moussa therefore made a choice of two filament pairs, related to the mean radius by the parameters °“o ) /$: 3 (1;, I/GZ The radii of these coils are C.) _ ‘3 R’I- 0(‘0 ) 2'2," 0(1: (79) and their distances from the symmetry plane are 2‘: Rafi: > 22,: 2'2 fi: (80) For any point on the symmetry plane r. ° . _ \— p / / {/C a WNW /OO%C///U////0fl/VOU/ //,/ /ui/ A —\\\\ \\\ \\\\\\\\\ \ :m m =< t\V\ .NGRN\\N\, m_x< u W 55 throughout the cross section of the winding. The winding procedure was as follows: The coil form was first mounted on a specially prepared spider and affixed to a slow speed lathe. During the winding the coil turned on a horizontal axis. Two annular rings were cut out of a large sheet of fish paper, with the inner diameter equal to the diameter of the coil mount and the outer di- ameter somewhat larger than the anticipated outer edge of the coil. These rings were coated with insulating varnish and cemented to the face of the coil mount, thus forming an insulating layer between the edges of the copper ribbon and the aluminum mount. In order that the mean radius of the finished coils, after winding and bakeout, be as nearly as possible equal to the calculated radii, it was necessary to estimate the winding thickness. This implies knowledge not only of the total amount of copper and paper in the winding, but also of the thickness of the varnish and its expansion as it dried. The coil mounts were made undersize, so a certain amount of insulation had to be wound on each to build up the radius before the first turn of copper was started. This permitted an adjustment for varnish properties and allowed a closer control in matching coil pairs. The thick- ness of insulation thus added can be found in Table I. Even with these precautions the finished radii of the coils devi- ate considerably from the ideal values. Primarily this is due to the uncertainty in thickness of the varnish impregnated 56 TABLE I. Focusing Coil Data W Coil Pair Au / A1 Bu I 81 Cu / C1 Du / 01 Mount 9.704 10.204 22.396 18.946 Radius 9.7035 10.204 22.396 18.945 Copper Width 2.000 2.000 1.400 1.400 Copper ' Thickness 0.0121 0.0121 0.0167 0.0167 Insulation Thickness 0.0056 0.0056 0.0067 0.0040 Number of Turns 116 116 57 64 Buildup Factor 0.0006 0.0006 0.0006 0.0006 Mount Buildup 0.0275 0.0275 0.1170 0.1130 before Winding 0.0250 0.0275 0.1125 0.1183 Finished 11.7920 12.3073 23.8490 20.426 Radius 11.795 12.306 23.837 20.442 ‘Winding 2.061 2.076 1.336 1.367 ‘Thickness 2.067 2.075 1.329 1.379 Mean 10.7618 11 .2694 23.1810 19.7415 Ihadius 10.7618 11.2688 23.1728 19.7526 Ideal \ All dimensions are in inches. subscripts refer to upper and lower set of coils, relative <> the z a 0 plane. 57 paper. The amount of varnish remaining on the insulation layers depends greatly on the tension maintained during the winding process. These deviations are unfortunate, but it should be pointed out that a deviation from ideal radius for a coil PAIR is much less serious than a mismatch between members of the pair. Therefore greater care was taken in matching the radii of the coil pairs and, as Table I shows, this has largely been accomplished. Care was also taken to choose the copper and insula- tion dimensions to obtain as nearly a square current carry- ing cross section as possible. A square cross section can be represented for the purpose of calculations as a single current carrying filament, which is nearly equivalent to the physical coil. A rectangular cross section coil, on the other hand, needs two filaments for an equivalent 3° With such coils the matching of the representation. focusing field shape becomes more complicated. With these preparations completed, a piece of copper ribbon about three feet long was cut at a 45 degree angle aJud silver soldered to the remainder of the conductor to Serve as the inner lead-in. The joint was carefully smoothed (“It to the same thickness as the rest of the ribbon, insu- 1fitted with tape, varnished and clamped at a predetermined Ihbint on the coil mount. The place on the coil mount was CI'losen to allow both leads from the same coil to be placed flat on tOp of each other, thus reducing their magnetic field, and to have the leads from all eight coils come out 58 in the same azimuthal direction. The plane of the leads was chosen to fall near the counter, in the space between the counter and the source. This choice minimizes the ef- fect of stray fields on the electron orbits. Figure 7 shows a schematic diagram of the main parts of the winding apparatus. Provisions are made for control— ling the copper ribbon tension and the amount of varnish carried to the coil by the insulation. The winding itself was a slow procedure. The coil was moved in approximately 120 degree intervals, with the conductor always securely clamped to prevent slippage. Micrometer readings were taken at three points around the circumference of the coil and the buildup of radius was recorded at frequent intervals. By varying the tension on the copper ribbon and the amount of varnish left on the insulation it was possible to con- trol this radius buildup from coil to coil and consequently to match coil pairs and approximate the ideal radii. The Change in radius of the winding contributed by the presence ‘1f the varnish was called the buildup factor for the coil. tanically the buildup factor was 0.0006 inches per turn. After the appropriate number of turns was placed cum each coil it was bound off with cloth tape, saturated w11th insulating varnish and again clamped securely. The filx'xished coils were baked overnight and then painted with aSir-drying varnish for protection. The coils then under- ‘Went an insulation check and also a dimensional check con- sisting of an extended series of micrometer measurements. 59 .mDP<¢ \ >Jaaam \\ zo;<.5mz_ \\ III Steam cmccoo hzmihmaao< zo_mzu._. 29.—Rho”. 60 Later on some of the protective coating was removed and the coils were checked turn by turn for the possibility of internal shorts. (c) The Coil Terminals and Leads The coil mounts for each pair of focusing coils are identical. Mirror symmetry arrangement thus requires that one coil of each pair be turned upside down. As all coils carry current in the same direction, the four inverted coils had to be wound in the opposite sense and care had to be taken that leads to all eight coils come out in the same direction. The coil leads were dressed as follows: First, the inner and outer leads of each coil were insulated from each other by individual wrapping with fish paper. Then they were placed tightly on top of each other and fastened together by tape. Thus each coil has a two conductor lead- in, with the conductors carrying current in opposite direc- tions, which reduces their fringing field. The main lead-in bus bar is also made of two con- ductors fastened side by side to a plastic strip. The con— ductors are brass strips one-quarter of an inch thick and two inches wide. Figure 8 shows a cross section of the lead-in bus and the connections to the focusing coils. 4.3 The Vacuum Chamber The spectrometer vacuum chamber is made from one inch thick tempered aluminum. It is cylindrical and roughly ALL SOLTS STAINLESS STEEL BRASS (4 PLASTIO BRASS . @L CURRENT FLDw L...J FIGURE 8. SCHEMATIC REPRESENTATION OF THE FOOUSING ,COIL POWER CONNECTIONS . 62 pie-shaped, formed by heliarc welding the various wall sec- tions to a flat circular base. A cross-sectional drawing of the chamber is shown in Figure 9. The chamber is mounted on the spectrometer mounting screws by an annular flange welded to the curved part Of its walls and located at its midsection. The internal chamber height is eleven inches. The upper edge of the chamber walls is machined flat and free of tool marks to form a good sealing surface for an 0 ring. The final smooth surface was achieved by hand lapping. The chamber is closed off by a lid, also made of one inch tempered aluminum and conforming to the pie shape of the chamber. The perimeter of the lid has two 0 ring grooves milled in it. Although original plans called for a double 0 ring seal, in practice only one 0 ring was found necessary. The 0 ring itself proved to be of non-standard length and all attempts at securing adequate quality custom-made rings failed, primarily, I believe, due to poor control over the vulcanizing process used by the manufacturers. The joints in the rings tended to have a knobby texture, with at least one place where the ring was thinner than normal, thus preventing a seal. Finally a satisfactory O ring was made from 3/16 inch diameter 0 ring stock. After careful measurement for length, to obtain a finished ring slightly shorter than the groove, the ends were cut on a bevel and ground flat on a high speed grind- ing wheel. The faces were then very carefully cemented together. An 0 ring made in this simple way has operated 63 i O /’ "“~ ,_ ‘4 ,/' \ ‘\ t/ /'/W (:5 \\ ‘I ‘ ' 4.1-31.-- $3333- ’ O a \ w J 7 / / / y /7 g \\ //I . / “ \ foiOUNTER /// FIGURE 9. SPECTROMETER VACUUM CHAMBER. 64 satisfactorily now for several years. The two flat portions of the chamber walls are posi- tioned at an angle of 270° with respect to each other. The faces of these wall sections are machined flat and bear 3.5 inch by 7 inch holes, centered on the proposed mean orbit of the machine, for mounting the source and the coun- ter assemblies. The outlet to the vacuum pumps is located near the counter end of the spectrometer chamber, to take advantage of differential pumping in the event of counter window leak- age. The opening allows a connection six inches in diameter. 4.4 The Source End Assembly A vacuum lock and a source holder were designed to enable the operator to change sources without breaking the main vacuum of the spectrometer and to position the source accurately in a fixed radial and axial position. The source lock consists basically of an all bronze 2.5 inch diameter gate valve, the type usually used for water service, modi- fied to make it suitable for use with a vacuum system. The seating surfaces of the valve were machined flat, with recesses for rubber gaskets and the stem was isolated from atmOSphere by strategically placed 0 rings. In practice this valve was found to be quite leak tight with the obvi- ous advantage of being non-magnetic and inexpensive. The gate valve is soft soldered onto a half inch thick brass end plate that fits over the source end opening of the spec- trometer tank and is sealed to it by means of a rectangular 65 0 ring. A separate vacuum line connection is made to the body of the valve permitting evacuation of the lock prior to opening. Referring to Figure 10, a schematic drawing of the source lock and holder, note that the end-plate contains a tapered hole, concentric with the gate valve and with its axis lying in the plane of symmetry of the spectrometer. The smaller radius of the opening is on the spectrometer side of the end-plate. The diameter of the hole is machined to be a slip fit for the source holder. Tapering the hole allows source position adjustment without binding. The outside face of the gate valve is soldered to a three inch length of cylindrical brass bellows, terminat- ing in a collar equipped with an internal 0 ring. The out- side Of the collar has the Shape of a square with vee grooves machined into the perimeter. A half inch thick brass frame fits over the collar, with about a quarter inch of space separating the two. The outside frame is firmly attached to the end-plate by four brass rods located at its corners. Adjusting screws threaded into the Sides of the frame and fitting into the grooves in the collar allow radial and axial adjustment of the source. The sources themselves are mounted on small alum— inum rings 1.25 inches in diameter. The rings are held in a recessed end of a thin walled aluminum tube, approx- imately three inches long. To minimize back scattering, most of the walls of this tube have been drilled away. 66 .>4m2wmm< ozw momnom MIL: .O. MCDOW— (A), h P2m2k0310< womDOw .._4<> mhr""~I-.‘.Iity feature, however, is not necessary in most cases. Th 3 Output pulses of the proportional counter are rather .zaonmmm Uco momsow ere .HH meswfim 6 9 small, millivolts in size, and thus high amplification is needed. The Geiger-Mueller counter is the simplest of the three. It provides large output pulses of essentially con- stant amplitude, its efficiency for electrons is near 100 percent and it can be designed to operate with very low 0n the other hand, it is by far counting gas pressure. Nevertheless, the slowest of the three detectors mentioned. in high resolution work we do not expect to encounter very high counting rates; this one drawback becomes relatively .minor, and the Geiger-Mueller counter is the natural choice for the spectrometer detector. (b) The Side Window G-M Counter The basic counter was designed by R. A. Parker at Vanderbilt University and a detailed account of its design 31 arm: construction can be found in Mr. Parker's thesis. Only a brief description is included here for the sake of comDle teness . Figure 12 shows that the counter has the form of a ridngt circular cylinder, one-half inch diameter and four in- Ches long, bored in a piece of 2.5 inch diameter brass stock. Part of the counter body is milled away to provide an open- idigi :for entering particles, and also to allow space for mounting windows and placing 0 rings for vacuum seals. '1' . he Inside bore of the counter is polished free of tool rks and forms the cathode. The anode is a 0.001 inch di Eirnfitter stainless steel wire, which can be exposed to the .C.DZ 70 F - . . l-S‘ure 12. The Side fljndow G-f’ Com ter. g- .._-_ ~_.fli-— — _. _ w-.. _ -i 71 counter volume in variable length from about 1/4 to 1 1/2 inches, thus allowing an adjustment in the active volume of the counter. The wire is supported at both ends by hol- low brass fingers, some 1/16 of an inch in diameter, which are highly polished and have rounded ends with a 0.005 inch diameter hole in them aligned with the axis of the counter. The brass fingers are held in alignment and at the same time insulated from the counter body by teflon plugs. A vacuum seal and the electrical connection to the outside is provided on each end by means of a glass to metal seals that are soldered to detachable end-plates. The end-plates seal against 0 rings. The body of the counter is drilled to provide a path for the continuous flow of counter gas and for evac- uation. An 0 ring fitted gas connection is provided at tine bottom of the counter along with a high voltage coax- 1a], connector. The counter and its window supporting plate are athatched to a flat end-plate which in turn fits against an 0 I3.1119 seated in a brass end-plate covering the counter end °5"3rling in the spectrometer vacuum tank. A proper position of the counter is ensured by a pair of brass locating pins. Attachment to the spectrometer is provided by means of two thurnbuscrews. Figure 13a shows the assembled counter. Figure 13. b shows the counter positioned on the spectrometer end- Plagg: 72 E1:; 5 r 3‘: h t a m er 0 Fir sure 13 (‘ 0) Con . Lter 1" ' ' ’— 4V1 1+ ( R‘ - .1 one. on Snecfi'owte T _ , v V‘- Y‘ ‘ M and Plnt :A e o 73 The vacuum side of the spectrometer end-plate is provided with a vacuum lock to enable the operator to change windows or to clean the counter without breaking the main vacuum. The gate assembly can be seen in Figure 14. The gate itself is a "C" shaped piece of flat brass stock, one- quarter inch thick, that slides against an O ring seated in the end-plate. The lock is guided by two rack and pinion gears, which in turn are driven by a right angle worm gear drive. The shaft of the worm is brought outside through a.rotating vacuum seal. A connection is provided to an GXternal vacuum line allowing the counter and the gate to be evacuated simultaneously, to reduce pressure stresses on the counter windows. (c) The Counter Gas Flow System As the spectrometer counter is of the self-quench- 1“9 type, it is necessary to provide a continuous supply Of counter gas to maintain stable operating conditions. Figure 15 shows a diagram of the gas flow system, together With lines provided for the evacuation of the source and the counter gate volumes. The counting gas, 2/3 argon and 1/3 ethylene is supplied premixed in a compressed gas tank.‘ The gas first passes through a pressure reducer on the tank itself and then to a metering valve V-l. The rate of gas flow is ‘ C ‘The counting gas was obtained from the Matheson °mpany, Joliet, Illinois. 74 Fj gure l4. Counter Gate System . 75 £qu; 33... 98 55:50 .0. mane... azaa xzap mac :33; 55:3 we. _ O. -> «33:3,. h..> 5592 a m n) x z < .F J. HT 5.3an fiWMT _-> Airs—MW «mimosa vi, m-> mu> mn> N-> pm. % g _ ., r - _ upw ..Omhzoo NKDP<¢ma1wP ....OO ozanoom ..N wane“. I Ml» >3 V o I + 9:st " _. Mn N v. a Leslrl Qozusom F Foldr x. U .. s. 1...: till. TH... _ 9.: oc Tlo>n¢ Sim amateur LTIi. + I -0255 5. . I, m w s. i v #:Iéll» 10'.“ X— rolu IH + 3x . r. F OJ >3 .YOIII. 04> n6 L CCCC m> .3 x m... A @255 O... o uuaaoo 04> o: o<> a: 90 five cubic feet, including a twenty percent safety factor. The gas load on this system is essentially unknown, thus as is done in such cases, it is assumed to be five cubic feet per second, or 150 liters per second. Allowances have to be made for outgassing of the system and for any obstruc- tions, such as cooling baffles and traps, placed in the vacuum lines. Outgassing and line impedance account for {about a factor of two in pumping speed and the insertion of a water cooled baffle in the line accounts for another factor of two. Thus the main diffusion pump should have a pumping speed of about 600 liters per second or more. Consideration of inlet versus outlet pressures for the main pump led to a selection of a booster diffusion pump with a pumping speed of 100 liters per second and a mechanical pump with a free air displacement of 150 liters per minute. Some time was spent in searching for a diffusion pump made of nonmagnetic materials to allow its location near the spectrometer. After about six months of negative results or promises of exorbitant cost, Consolidated Electro- dynamics Corporation brought to market a six inch stainless steel three stage fractionating diffusion pump, the PMC—721,‘ 4 with a pumping speed of 700 liters per second at 10' torr, using silicone fluid DC-704.°° This pump was selected as the main pump for the spectrometer. °Consolidated Electrodynamics Corporation, Rochester, New York. “Made by Dow Corning Company, Midland, Michigan. 91 The booster pump chosen was also made by Consoli- dated Electrodynamics Corp., type MB—lOO. This pump is made of ordinary steel and was therefore placed at the end of a ten foot long vacuum line and located outside the sphere enclosed by the compensating coils of the spectrometer. The mechanical pump chosen was the CBNCO Hyvac l4.° (b) The Vacuum System Figure 22 shows the salient features of the vacuum system. The spectrometer tank is evacuated by a six inch diameter brass pipe, connected to it and to the diffusion pump by bolts and 0 rings. A water cooled baffle is inter- posed between the tank and the pump. As commercially made baffles turned out to be either too expensive or made out of magnetic materials, this baffle is home made. Figure 23 depicts a section through the baffle as it was originally designed, with three stages. Later, after about a year of operation it was found that one stage was quite suffi- cient for our purposes. The upper two stages were removed, yielding a slight increase in pumping speed. The exhaust of the main diffusion pump passes through a ten foot, three inch diameter line and enters the booster diffusion pump, which is located some twelve feet from the center of the spectrometer. The booster pump is connected to a ballast tank, to reduce the effects of gas surges, and finally exhausts into the mechanical pump. 'Central Scientific Company, Chicago, Illinois. SPECTROMETER . ION GAUGE VACUUM TANK 6 IN. DIAMETER 54 IN. LONG PUMP LINE WATER COOLED BA F FL E MAIN DIFFUSION PUMP SIN. DIAMETER I20 IN. LONG PUMP LINE P—D THERMOCOUPLE GAUGE BOOSTER DIFFUSION PUMP BALLAST TANK 2 CU. FT. - NORMALLY CLOSED SOLENOID VALVE A wIRED TO FOREPUMP MOTOR FOREPUMP FIGURE 22. BLOCK DIAGRAM OF THE MAIN VACUUM SYSTEM 93 M U P DIFF. HIGH VACUUM WATER COOLED BAFFLE. FIGURE 23. 94 Vacuum is protected by a solenoid valve connected to the intake of the mechanical pump and coupled to the motor. The valve closes upon power failure. During the past three years of operation of the vacuum system it was found that the local water supply contains enough minerals to do extensive damage to the diffusion ,pumps. Boilerstone was discovered at one point to have «completely blocked the water cooling lines of the main dif- fusion pump, causing severe overheating. The lines could not be cleaned and had to be completely replaced. off similar occurrences in the future when they might inter- To ward fere with an experimental run, it was decided to place both diffusion pumps on a closed cooling circuit and use distilled water. A large heat exchanger, made entirely of copper and aluminum (found in the University's salvage yard), was im- mrsed in tap water cooled copper tank, its lines were con- hectted to a small rubber impeller circulating pump‘ and a Pressure switch was provided to shut off the pump and the heasters of the diffusion pumps in case of coolant loss. (c) Electrical Controls and Associated Equipment The electrical circuit used to control the vacuum Pumps is a sequential self-protecting type, shown schemat- ical 1y in Figure 24. The circuit breakers are used as power switches for the mechanical vacuum pumps. The sequence \ Ave ‘Pump made by Sherwood Brass Works, 6331 E. Jefferson ‘ s Detroit 7, Michigan. 95 .5350 ..oEzoo ease 3229; TN maze...— . .ZWQO Izllll ...-Isl .. u 0mm 2 2.3:. to ezuzoezoo " ze . .ommoso Buasmoz rots” zotsmrwse . one ..oEzoo $3.. .6528 .25.. 553 2.303 zoosta «memoom zoasuua 2.4: arse .36:qu ease \/ a331m¢0u Suhw>m I / \IIIIIIK (IIIIIII/ \llllll _ / Z-(Z muhzaoo ' ’ ’ .mhI .KPI :3 :3 .: nzw 20 «m 20 .m 3 N 20 O... [8 Omn— Oma \. L i. i H mm mm ~m\ T «m @omz one one to one to rot: mmammume _ m E o a: . M j Trees L N 3659 N (Pg 08» o: I} 96 requires that the spectrometer forepump and the diffusion pump water must be turned on before the heaters of the dif- fusion pumps can be activated. The heaters are switched on by means of self holding relays and therefore even a temporary malfunction, such as a power failure or water pressure drop, will disconnect the heaters. Continuous readings of the pressure in the spec- -trometer tank and in the foreline can be made by means of a combination ionization and thermocouple gauge.‘ The ioni- zation gauge tube is located inside the tank, mounted on a glass to metal seal and attached to the source lock end- plate. This location protects the tube from damage and .1xzsures a very short connection to the vacuum system. \ IotldL ‘Consolidated Electrodynamics Corporation GIC-llo ==ation and Thermocouple gauge. . . . I II II III I: III: II I III-ll I .II III] IIIII Illlll ‘III. 1 II]! CHAPTB R 5 FOCUSING COIL CURRENT CONTROL SYSTEM 5 .1 Introduction The Michigan State University spectrometer is de- signed to use focusing coil currents from 0.3 to 60 amperes. This current range corresponds to an energy range from 250 The determination of electron line e.v. to nearly 2 Mev. 5, with the spectrometer momenta to within a few parts in 10 adjusted for a resolution of about 0.05% requires a long term stability of the focusing magnetic field of one part in 105 or better over the entire current range of the in- Strument. Furthermore, to realize the full high resolution POtential of the instrument, line broadening due to short farm fluctuations in the focusing current have to be kept low, preferably to one part in 105 or less. At the time Of construction of the spectrometer no power supply meet- ing these requirements could be obtained from commercial 3‘D‘J-lrces at a reasonable price. Its design was therefore u“dentaken by the author. As transistors were beginning to l<>ok attractive in high power applications, the decision "as made tO abandon the usual configuration of web current sources, namely a regulated d.c. generator supply with vacuum 3e noise reduction and regulation circuits, such as those de yeloped by Sommers et al.,32 in favor of an all transistor 97 98 power supply. Other possibilities, such as batteries were discarded as too unwieldy. The basic design of the current regulator follows quite closely a circuit developed by Garwin and his co-workers at Columbia University.33 The accessory equipment such as power input and field regulation loops combines original 34 designs with those developed for the Vanderbilt machine. A block diagram of the entire control circuit is shown in Figure 25. Three phase 440 volt A.C. power is first stepped down to 120 volts and rendered variable by a. saturable reactor. The output of the saturable reactor is fed to a three phase full wave rectifier bridge, filtered by a two stage L-C filter and passed through a set of power transistors which serve as the fine current regulator. The current then goes through the focusing coils and finally returns to the power supply. Two main feedback loops main— tain current stability. A coarse loop, Operating the sat- urable reactor and activated by error signal derived from the voltage drop across the power transistors and a fine 1009. deriving its error signal directly from the field °f the spectrometer . The remainder of the chapter is devoted to the de- scription of the various parts of the current control SYS’ teal- 5.;3 . £92.12?" and Construction of the Transistorized Power \EEEJ. (a) The Input Section As was mentioned above, the regulator itself was 99 .mN mmawi .532...“ euros ruemzomeounm no Samoa; recom szo. en o<> o: use area 92 ampere. we .53 o4 unu<> amour: mob: .o .o ezmmmso 55:8 I .2323 H I»? 53349. _ I. + 3956 news: Zn .336 uozmemuum ms on. . 5.5.53 _ .Zzo; o 4 . . o.— comxm I r 3-33 :5 5.20.2. .31 100 patterned after a design by R. L. Garwin.33 The circuitry was modified somewhat to suit our particular application. The entire power supply will be described in the sequence laid down by the block diagram of Figure 25. The power supply uses a 440 volt three phase input. The choice is a fairly logical one, for it enables the en- tire power supply to be built into a rather small package and saves the cost of a 10 KVA motor generator. The 360 cps ripple produced by the rectifiers is not much more dif- ficult to control than generator noise and ripple. The 440 volt input was chosen to insure the use of one of the primary power lines in the physics building, to minimize fluctuations caused by other equipment connected to the same line. The 440 volt input is stepped down to 120 volts by a three phase transformer that serves only the spectrometer. The 120 volt lines are led from the basement Of the building to a distribution panel near the control desk where the rest of the power supply is located. The voltage drop in the lines is quite appreciable, about 25 volts, when the power s“Dilly is set for maximum current. This limits the focusing 9°11 current to about 58 amperes. Eventually it is hoped to locate the step down transformer at the control desk also, to eliminate these losses. With full 120 volts available, one should be able to Obtain about 75 amperes through the fack‘lsing coils . (b ) The Rough Regulator The complete regulator is basically a double loop 101 servo mechanism. The primary, or rough loop, establishes a small region of current over which the fine regulator Operates. The rough regulator has a low gain and is mostly non-dissipative in nature. high gain and performs its function by dissipating some It is because of this power dis- The fine regulator loop has of the available power. sipation in the fine regulator that the rough loop is needed. Otherwise, the overall efficiency of the regulator would be low and its range would be limited by the power dissi- pation in the power transistors. In the present power sup- ply which uses 10 power transistors in parallel, the per- missible power dissipation is about 250 watts. To keep it from rising above this level, it is necessary to limit the voltage drop across the power transistors to a low value. The figure chosen on the basis of transistor characteristics was 3 volts. The function of the rough regulator is to maintain the voltage drop across the power transistors at approximately this level. The circuit diagram, Figure 26, Shows the main features of the rough regulator. The tran- sis tor voltage drop is sensed at the power transistors. Long cables or remote grounds should be avoided here, since any additional error signals, caused, forexample, by pick- off from the power cable may lead to unstable operation. I?“5 :sensed voltage drop is added to a three volt battery am": Elmplified by a simple transistor D.C. amplifier which 35 The is a- modification of the original Garwin circuit. D. C ‘ amplifier operates three parallel power transistors 102 Figure 26. Schematic diagram of the spectrometer power supply. 103 on case: 5&8 euros mmfizomeomem Greta Cuzoa: ezuzezewn Sardine. So .8. 5.3.53: .382: . I .P , . JPN W . mice .- . 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L JXF 83) W MHCJ T92" _ . \ _ Fonz. o . _ _ _ mcuxduco + (Icon 0“ o .I cc 33.83. euros «33:3. “2; are 3.28 a!» .hudxw Ctr—(box Nth .m¢O-.m.ml(¢h MM(& Oh COPU‘UK ¢U3¢OKGZCCP «use... 02308 x...) 35045;- 5.6: uuoI Izo «uses 33:33 2309 an; 104 as a current ”valve" which controls the output of a 24 volt magnetically regulated power supply and hence the d.c. ex- citing current through the control windings of the saturable reactor. The circuit operates as follows: A low voltage drop across the power transistors lowers the current to the base of T15, causing the emitter-collector voltage to increase, thus causing an increase in the base current of the driver transistor T16. Current through T16 rises and thus increases the base current to the "current valve“ tran- sistors T17, T18, and T19. The impedance of these power transistors drops, allowing more current to pass from the 24 volt power supply to the control windings of the satur- able reactor. The reactor, in turn, supplies more current to the rectifier bridge, more current flows through the pass transistors and the voltage drop across them is restored to the desired level. Three power transistors are used to control the current supplied by the 24 volt power supply, since they must be able to dissipate all the power provided by this supply, about 80 watts. Normally just one power transistor could provide this control alone, as a 2N278 can dissipate about 86 watts. However, the 24 volt supply has very large turn-on transient, thus three transistors are necessary for safety. (c) The Fine Regulator Loop The fine regulator loop serves to establish the desired magnetic field in the focusing coils and to maintain 105 it at a predetermined, fixed value. The error signal for this loop is derived directly from the focusing field of the spectrometer. In principle, the fine regulator works as follows: Two separate alternating current signals are deve10ped by two rotating search coils mounted on a common shaft and rotated at the rate of 23 revolutions per second. (This system is described in detail in section 5.3.) One of these coils is located near the electron orbit radius in the spectrometer, and its output is therefore directly proportional to the spectrometer field. The other search coil is rotated in the field of a permanent magnet and thus produces a constant amplitude reference signal. The orien- tation of the search coil axes is such that the two signals are 180° out of phase. In practice, a known fraction of the reference signal, chosen by the Dekavider, a linear Kelvin Varley voltage divider,‘ is matched against the spec- trometer coil signal. The difference is filtered and am- plified and serves as the error signal. The error signal is then demodulated synchronously with respect to the ref- erence signal. The demodulator output has positive or neg- ative polarity, depending on whether the spectrometer field is higher or lower than the desired value. The output sig- nal is filtered and fed into the transistor D.C. amplifier of the regulator. 'Electro-Measurements, Inc., Portland, Oregon. Model RV-622. Linearity i 0.001% at 0.5 watt or less, resolution 0.0001%. Input resistance 10,000 ohms. 106 The raw error signal emerging from the Dekavider contains a great deal of noise and harmonics. While the desired 23 cycle per second sinusoidal signal is small, of the order of microvolts, the undesirable noise may have amplitude equal to an appreciable fraction of a volt. Aside from amplification, the signal must therefore be extensively filtered. The most obvious and straightforward method of ac- complishing this is by use of tuned amplifiers. High gain and very narrow frequency response are relatively easy to achieve. These could not be used, however, for two reasons: First, the rotating shaft does not hold its speed perfectly constant. Small shifts in the flipcoil frequency, when passed through twin-tee or L-C filters, may result in large phase angle changes. The phase detector perceives these changes as bona fide changes in the error signal, causing variations in the focusing field. The second reason is related to the speed of response of these amplifiers. Any amplifier is degraded in stability by introduction of pos- itive feedback. High gain band-pass amplifiers are no ex- ceptions. Their response to a step change in the amplitude of the pass frequency signal is slow and frequently tran- sients will induce ringing. The spectrometer regulator requires that the response speed of the fine loop be faster than the coarse loop, otherwise instability will occur. The rough regulator will cause the power supply to overshoot the balance point before the fine regulator loop can stop 107 the current from changing. All the tuned amplifiers that had sufficient gain for our purposes were far too slow. All feedback type file tering had to be abandoned. Instead, we used series filters, in a more or less brute force approach. The efficiency of this method is much lower, as all filtering elements intro- duce losses into the circuit which have to be compensated by an increased number of amplifying stages. Nevertheless, this system has better stability and higher response speed to amplitude changes in the error signal. Figure 27 shows the details of the fine regulator loop. After mixing at the Dekavider, the raw error signal is fed to a General Radio transistor preamplifier,’ operated on the "flat" frequency response setting. Output of this amplifier is bridged with a 4 mfd capacitor that shunts the high frequency noise, and then is fed to a voltage ampli- fier." A power amplification stage with tuned transformer coupling brings the error signal to the phase sensitive detector. The phase detector, or demodulator has proved to be a critical part of the feedback loop. Initially a 34 was used. In this design developed at Vanderbilt by Nall circuit, the reference signal was passed through a cathode follower for isolation, and then amplified by two parallel 6L6 push pull stages, with transformer input and output. ‘General Radio Tuned Amplifier and Null Detector, Type 1232qA. "General Radio Unit Amplifier Type 1206-8. 108 Figure 27. Schematic diagram of the error signal ampli- fiers and the phase sensitive detector. 3 853s .mOFUMPmo m>_:wzww ww1wr<§¢wn 110 Output of the power stages provided, in principle but not in practice, a sinusoidal plate voltage for a pair of de- modulator triodes. The error signal was introduced to the grids of the phase detector tubes also by transformer coup- ling. The difficulties with this unit were, on one hand, an apparent degradation of the transformers with time, due to unknown causes, and on the other hand, very poor fidelity at the 23 cps frequency, leading to grossly distorted wave- forms. Drifts were observed in the demodulator stage which tended to change the bias level required by the regulator's transistor preamplifier. Rebalancing the demodulator would produce a change in the magnetic field of the spectrometer. This unit was therefore abandoned in favor of one free of these objections. The new phase detector unit which is presently in operation, uses a mercury wetted contact relay as a synchronous chopper. A chopper operates as a nearly ideal rectifier; its forward resistance is very low, its back resistance essentially infinite. The contact resist- ance of the relay contacts is of the order of 50 milliohms and stays constant to within S milliohms. Dissipative losses are therefore almost eliminated. Furthermore, during the conduction half cycle when the relay contacts are closed, the chopper does not introduce any waveform distortion into the error signal. Figure 28 shows the circuit diagram of the chopper and its driving circuit. The reference signal first goes through a phase shifter. Two triode phase mix- ing stages are used, V1 and V2, giving a total phase shift 111 Figure 28. Schematic diagram of the chopper driving circuit. 1:12 .mZmo amen—CID mu 8:3.— mao mm mm» aim uni... >08 .7 «waaoru «$5.30.... mooxuko muooih ...:zxom 4h? ./.. moz<400» .... 113 of about 270°. After the phase shifters, the signal goes to a Schmitt trigger, where the sinusoidal reference signal is converted to a square wave (V3 and V4). A neon lamp is included for visual check of trigger operation. Square driving voltage is needed for proper operation of the chop- per, insuring prompt closure of the contacts. For maximum output, the chopper must be synchronized with the zeros of the error signal sine wave. With a sine wave drive a normal mercury wetted contact relay will not pull in at a precisely constant phase angle, causing a Jitter in the output waveform. The output of the Schmitt trigger is power ampli- fied by a cathode follower V5 and fed through a suitable network to the coil of the chopper. The chopper has a two section coil; a d-c current, passed through one section of this coil, can be used to bias a magnetized core of the relay armature and hence to change the dwell time of the two switching positions. The 100K variable resistor is used to vary this d-c bias current and hence the chopper balance. The d-c signal developed by the demodulator is an average of a full wave rectified 23 cps signal and hence is basically a 46 cps signal. Virtually all of the 46 cps component is removed right after the demodulator by a twin tee network tuned to this frequency. The remaining ripple is further minimized by a 3000 mfd capacitor placed across the input terminals of the transistor preamplifier that serves as the fine regulator input. 114 (d) The A.C. Feedback Loops Although the fine regulator loop has a very high V gain, of the order of 107, it has a rather poor frequency response. In fact, due to the long time constant of the filters situated after the demodulator, the response of the loop is poor for any signal with a period appreciably shorter than 0.25 seconds. Such conditions render the regu- lator incapable of removing noise and ripple from the sys- tem and almost always lead to instability. Moreover, in a two loop servo-system such as this one, slow response in the fine loop combined with relatively fast response . of the rough regulator causes overshoot of the error sig- nal balance point. If the response mismatch is bad, we will get low frequency, large amplitude oscillation. As the time constants of the loops are brought together the oscillations will diminish in amplitude and may increase in frequency by a factor of two or so. Finally, with the fine loop faster than the coarse one, we can get stable operation. To aid in stabilizing the regulator and to restore its frequency response, two parallel a-c feedback loOps were added. As can be seen from Figure 26, these bypass the fine regulator entirely. They derive their signal from the positive terminal of the power supply and provide high _a-c degenerative feedback for the system. The choice of component values for these feedback loops proved to be rather critical. Considerable length 115 of time was spent in the effort of securing stability against transients over the entire current range of the power supply. To match the time constants, 4000 and 2000 mfd capacitors were needed, connecting the positive end of the supply out- put to the input of the preamplifier through a 500 ohm rheo- stat. In parallel with this loop is another, consisting of two 10 mfd oil filled capacitors in series, also connected to the positive terminal of the power supply and entering the preamplifier through a 50 K variable resistor. This loop is chiefly responsible for high frequency noise feed- back. This combination gives a nearly critically damped response to the power supply. (e) Fine Regulator Construction Notes The regulator is constructed in two basic parts: the power handling section and the preamplifier. The main power transistor section with its drivers, and the power transistors belonging to the rough regulator are placed on copper fins suspended in a bath of transformer oil. A 1/4 inch copper tube circulates tap water in the oil tank to remove excess heat developed by the power section. Cur- rent equalizing resistors are soldered directly to the emit- ters of the power transistors and connected to a common bus her, also immersed in the oil bath. Although each of the power transistors can carry a collector current of 14 amperes, it is only required to pass 6 amperes or less. This gives a better than 100 per cent safety overload fac- tor and, in addition, operates the transistors in a region 116 where their gain is higher. (The 2N278 beta begins to fall off at high currents.) The preamplifiers for the main sup- ply and for the rough regulator are built on separate ter- minal boards and connected to the front of the oil tank by a multiterminal Amphenol connector. The preamplifier section is detachable for ease of servicing. (f) Regulator Operation The regulator works as follows: when the spectrometer field is smaller than required, the net error signal is in phase with the reference signal, and the output of the de- modulator swings negative. Current flows through the filter described above and then through the 1000 ohm input resistor of the transistor preamplifier and then to the base of T1 (refer to Figure 26). This turns T1 to a more conducting state. The collector current of T1 increases, decreasing the base current of T2. This action decreases the collector current of T2 and causes the base of T3 to go more negative with respect to the emitter of T3. This change of potential in T3, the first driver, causes an increased current to flow between the collector and the emitter of T3. This current is amplified in T4, the main driver transistor. T4 causes higher base current to flow to the bases of the pass transistors T5 through T14. This biases the power transistors to a more conducting state and consequently . the voltage across the transistors drops. The rough regulator senses the voltage drop across the power transistors as being insufficient, and in a manner 117 already described above, begins to turn on the 24 volt power supply and hence the control current through the saturable reactor. The saturable reactor begins to drive upward in- creasing the a-c input to the rectifiers, and increasing the current output of the power supply. As the balance point is approached, less current flows to T1, more current flows in T2, the driver bias decreases, causing a decrease of base current in the pass transistors. The voltage across the power transistors increases causing the rough regulator to slow down and stop its power increase. The desired value of field in the spectrometer is thus reached. Any further increase of the current will cause an Opposite shift in the error signal, which in turn would demand a decrease in the current. Thus the error signal tends to monitor the current. Frequently, during large downward changes of cur- rent, the error signal amplifier circuits overload and cut off the preamplifier. In such instances the voltage across the power transistors will tend to rise (the transistors are biased to cut off) and the power dissipation of the transistors may be exceeded. To prevent this, a Zener diode is connected from collector to base of T3, which will conduct whenever the voltage across the transistors exceeds 6-8 volts. The diode acts as a base to collector clamp. As soon as the signal to the preamplifier reaches a lower level, i.e., when proper operating information is restored and the voltage across the pass transistors drops, the diode stops conducting and the regulator functions normally. 118 The regulator is connected to building ground at the emitters of the power transistors. This means that the cable leading from the power supply to the spectrometer is floating above ground by the amount of voltage drop in the auxiliary shunts. Likewise, it should be noted that the "common" of the preamplifier floats approximately three volts above ground and therefore the output of the demodu- lator must likewise be floated. The regulator is interlocked to the water flow for oil tank cooling and to the switches that control the ro- tation of the shaft, the B+ supplies and the 24 volt supply of the rough regulator. Failure of any of these will cause an immediate shutdown. 5.3 The Rotating Coil System (a) Introduction The heart of the fine regulation feedback loop is the rotating coil system. This system is comprised of the field sensing coils, the rotating shaft and its drive, the permanent magnet which provides a reference magnetic field, and, finally, the temperature control of the magnet and the rotating coils. At first a modified capy of the Vander- bilt rotating shaft system was built, similar to the one described by Nall.34 This shaft was still in place when the first overall spectrometer photograph was taken. It can be seen in Figure 5. A number of difficulties finally led to a complete redesign of virtually all of the elements 119 of the system. First, the Vanderbilt system used a Vee belt drive which proved to be too rough for us, and had to be replaced with a flat endless nylon belt. Second, perhaps due to bad luck in obtaining material for the shaft, our shaft suffered from excessive vibration. The six foot long shaft sections had to be shortened and two extra bear- ings added. One of these had to be made non-magnetic as it was located too near the spectrometer. This bearing never was completely satisfactory. Third, the spectrometer coil was originally held between two porous bronze, self aligning sleeve bearings which could not hold it in a fixed position with respect to the spectrometer. A simple calcu- lation shows that a radial motion of the spectrometer coil of 0.0025 inches will shift the spectrometer field by one part in 104, i.e., ten times the allowable amount. At one point we did manage to find a pair of stainless steel ball bearings and replaced the bronze sleeves by these bearings. Although the quality of the bearings was low, the perform- ance of the shaft improved somewhat. Finally, detailed examination of the system found the shaft torsionally so flexible as to show an appreciable deflection when the lubri- cation properties of the bearing changed (as would happen, for example, with a temperature change). This made it im- possible to hold a fixed phase relationship between the two rotating coils and made the entire system nearly useless. Thus after several months of tests and modifications, in an attempt to save the time and funds invested, this shaft 120 had to be abandoned and the design of a new shaft was under- taken by the author. Its design and construction features are found below. (b) The Field Sensing Coils Quite frequently, when one is dealing with nonuni- form magnetic fields, the objection leveled against the use of a rotating coil as field measuring device is that it measures the average field over the area of the coil, and its output is therefore rather rich in harmonics. Special coils have been developed, however, that yield an output signal corresponding to the value of the magnetic field at the geometric center of the coil. Such are, for example, the "fluxballs."36’37 The fluxball is a spherically wound coil with a variable density winding. It is rather diffi- cult to make. A similar behavior in a nonuniform magnetic field can be obtained by using a cylindrical coil of care- fully chosen dimensions.38 If the length to diameter ratio L/D is equal to 0.72, the coil will behave very nearly as a fluxball. The inner diameter does not affect the per- formance appreciably as long as it is less than half of the outer diameter, a condition which is easily satisfied. This type of coil is used with the spectrometer. As was mentioned above, the error signal is gener- ated by matching a known fraction of a signal developed by a coil in a permanent magnet field to the signal develOped by a second coil in the spectrometer field. This requires a choice of design parameters, namely, the dimensions of 121 the coils, the optimum wire size and its resistance and the value of the permanent magnet field strength. The fol- lowing calculations show how these parameters may be deter- mined: Considering a general case, the E.M.F. generated by a search coil is: Emma: = ‘9 é max where (84) a) - angular frequency of the coil Qua maximum flux linked by the coil. Considering the coil to be built up of cylindrical windings of radius $3 , having n turns each, then for each layer: @mx ewe n8 3 he: (85) where B is the strength of the magnetic field, L is the length of the coil layer and d is the diameter of the wire and insulation. For a coil of inner radius R0 and outer radius R, the num- ber of layers will be N __._______‘2"R° (86) L d.+t where t is the thickness of the insulation between succes— sive layers. The number of turns on the coil is LUL-R-o) Nt=nNL=dw+J (87) I To calculate ém“ 1‘ Z §K max consider the radius of K th the k layer: 122 pK=RO+(2K.—I)r +(k—‘\)t r=§z g 2-2. ‘¢d+t L L. _ émax . Z n.3," .5; B AK ) (AK-1) (88) K=| K By use of (88) K: R-f. _ TLB _ _ 2 @mx- 2r 20+(LK |)Y’+(K |)t]AK K=| . "(LB K=§-;—R€-~'/z. 2. (89) 2‘)??- J [K(2r+t)+(Eo*V‘-t)] dK. K-‘yz Call 2r + t a T and note that T is small. ’R’LB M3 Ram—RR." 2. 2, as —-——— + +- E. .-R,+JZ° + <¥nmm. Eir [ 3T. 'T R' Since (Ro - r - t) z R0. Only the first two terms are significant, since T is a small number. =1LB... 3.. [Z3 . 3d(d+’t) (R e) (90) The E.M.F. generated by this coil is ’R’LB EMGX = 3d1dfig) (R3" R03) (91) 123 The length of wire contained in this coil is R-Bo K= 27:; L = E I. A K where - (92) w K. (=1 l; —- 2~ —L—- K — “ PK 2,- is the length of wire in each layer. With the help of (88), K = “'2 0/2.r+t LW=T YLZ. (2° +[ZK‘|]T+(K—I]t)AK {:4 Rio a N TL. i: 2T+C _/2’ “T J [K(Zr+t)+(Ro-r-t)14( (93) K-='/2. Keeping only the dominant terms we have A. 11:._ 7'- 1 (94) Lw ‘ June) )2 2°) If the radius of the bare wire is r' and the resistivity of the wire is $9 , the resistance of the coil is I .Lw = PL =§_ rlz'al(d+t) (R2_R:) (95) In our coils t s 0, and L a 1.44R, Ro - R/4. Summarizing we have: 2‘ Emax 1’ "484 j: w (95) 3 Lw 24241{% an ‘2; RC. 3 (“350 ‘rIzdz 3 (98) 124 So far the calculations refer to a general case. In particular, considering the spectrometer feedback loop, it should be remembered that the permanent magnet coil is connected across a 10,000 ohm load, the precision voltage divider. Therefore it draws current and its resistance must be included in calculating the net output voltage avail- able out of the divider. The spectrometer coil, on the other hand, does not draw any current at the balance point, and its resistance is therefore immaterial. Consider the diagram: qu1(pM) RD gout (RM. ac ’ Rc stands for the resistance of the coil and RD is the re- sistance of the voltage divider. _ '30 gouthM.) ... R'C. + RD amok (P.M.) E ) should be equal to the E.M.F. of the spectrometer out(P.M. coil, when the spectrometer is operating at maximum current, thus Ema: (SR) = E4m: (P.M.) 4 4 2 _. 2. ”84 d;P 8"“) - 23E»... . ”84 R2?” BMW ‘9 29+l'35 2. 2. . §’ d RM. . Y" ARM. 125 It is also possible to maximize Bout’ with respect to R to obtain the best coil diameter. This calculation leads to the equation: d 800t(P.M.) d2 fi=0 3 E=Z°56xl05(r'd)’/3 Numerical calculations show that this maximized type of (99) coil can be realized only with some difficulty. For the available magnet gap of 2 1/4 inches, allowing for the hous- ing which must hold the coil in place, the maximum possible R is about 1.4 cm. The optimum wire size for this coil would be number 44 which is rather difficult to handle. Also, the coil resistance would then be about 40 K ohms *1\ and the coil would therefore be very heavily loaded by the voltage divider. Internal heating of the coil may be ap- preciable in this case, for several milliamperes would be drawn from it. Any changes in resistance would produce errors in the size of the standard signal. Furthermore, the signal change arising from area and resistance changes due to temperature is more pronounced as the coil resistance is increased, thus requiring a closer control of the tem- perature of the wire in the coil. For ease of manufacture and the reasons mentioned above, a compromise solution was used. The wire was chosen to be number 40 for both coils, one coil being slightly larger than the other. The spectrometer coil, as it oper- ates in a nonuniform field was made with L - 1.44 R as closely as possible. The permanent magnet coil was ‘\ 126 dimensionally similar to the spectrometer coil, except for having a larger number of turns. The L/R ratio does not have to be adhered to too closely here, for the field of the permanent magnet is relatively uniform. The following values were used: 6 ohm'cm, 9‘ - 1.72 x 10' r' a 5.05 x 10"3 cm, d - 11.2 x 10'3 cm, 8 Max. Spectrometer field . 260 oersteds - 260 x 10' webers/cmz. 8 Permanent Magnet field a 360 oersteds - 360 x 10' webers/cmz. (This was the field of the permanent magnet when it was de- livered to us.) 09 a 145 rad./sec. RD - 10,000 ohms Rs - 1.4 cm. The calculated radius of the permanent magnet coil is RP== 1.45 cm. The coils were wound by Abrams Instrument Co. of Lansing. During the winding it was not possible to keep perfectly even layers with such small wire. Thus for the calculated lengths of wire, 5600 feet and 6550 feet for the spectrometer and permanent magnet coils respectively, the radii came out to be nearer 1.5 cm. As field measure- ments at a point were not an absolute necessity, the coils were allowed to pass. The resistances of the coils are 6870 ohm5 for the permanent magnet coil and 5900 ohms for the spectrometer coil. The voltage developed by the 127 spectrometer coil is E Sp g 31 volts and that developed across the divider by the permanent magnet coil is Bout p M g 32.5 volts. The coils thus nearly satisfy the Bout P.M. e E requirement for maximum setting of the spectrometer max Sp. current. (c) The Rotating Shaft System (i) The rotating shaft, its drive and supports After the rather unfortunate experience with the rotating shaft made of aluminum tubing, a solid, carefully machined one was designed and built, using precision ball bearings wherever possible to insure smoothness. The shaft is built in two sections each six feet long, and is carried by three main bearing supports, one self aligning ball bear- ing at the permanent magnet end, two ball bearings strad- dling the drive pulley which is located at the center, and a double beryllium c0pper ball bearing located at the spec- trometer end. The two shaft sections are made of Alcoa 7075 alu- minum alloy in the T 651 temper.‘ This means that the orig- inal bar stock pieces received heat treatment, and were subsequently straightened and stress relieved. This is an important consideration, when a considerable amount of machining is to be done. This alloy is a special high ten- 3116 strength aluminum alloy, having an ultimate strength of 77,000 psi, the highest obtainable. It is quite free ‘ 'Aluminum Company of America, Pittsburgh 19, Penn- sylvania . 128 machining, and takes an excellent finish. During the original design period, cast shaft sec- tions were considered, since it was reasoned that they would provide good rigidity to shear; however, none of the local foundries were able to cast a blow-hole free specimen and so the idea was abandoned. After some concessions to the limitations of the physics department's machine shop facilities, the shaft sections were designed in tapered form, using a stepped taper. Each section consists of 18 straight sections of successively smaller diameters, as shown in Figure 29. The reason for tapering the sections is to remove weight at the ends near the search coils, especially at the spectrometer end where limited load bearing capacity bearings have to be used, and to prevent uniform-shaft transverse vibrations as much as possible. Analytically the shaft sections were treated as smooth tapers. As the search coils must be kept in a fixed angular position with respect to each other within a few seconds of arc, it is of some interest to find the torsional deflec- tion of the shaft as a function of torque. For a uniform cross-section shaft we can write _6..L 9" e where (9 is the torsional deflection of the shaft in radians, 0,, is the specific torsional deflection, R is the shaft radius in inches and L is the shaft length in inches. an is defined as follows: 129 .kudzw 02:.<.r0m NIP A >420 0....(2mrom “.0 zo.._.omm .mN Mano...“— w4<0m 0... P02 . 130 __ 7‘12. 0.. ‘ _‘GJ— (100) where T is the torque in 1b-in, J is the polar moment of 4 inertia, an engineering term defined as .T = g E. for a circular cross section,‘ and G is the shear modulus of the material. Thus __ L. 9 ~ 6.7 (101) Between two cross sections of a shaft a distance dx apart, the angle of twist d6 is: d9 = ...I.— dx , so between ends A and B, J (; B T ( 2) 6%A8 ~[A (SST This expression may be used to calculate 6 for shaft of variable radius. R is implicit in J since J'==%E-Fl4 for circular cross section. Thus for a tapered shaft as shown in Figure 30: Rx ...- R(a +xta“°( (103) 2;. - Re tam“ = L. (104) ’- L 6 e I. 311‘. = .21. Ax (105) G J «G “(33 0 o ‘J is the moment of inertia per unit mass, multi- plied by the cross sectional area of the cylinder. 131 FIGURE 30. SCHEMATIC DIAGRAM or A SHAFT SECTION. 132 L 9 ==_§J: doc __ we 0 (2. +2 tandy‘ 2. T‘L. ‘ I ._ .1. 3 fl’G (‘2‘: R6) 203 RE (106) For our case G 2:3.5 x 106 lbs/inz L a 72 in R0 3 00875 in RL ' 10938 in In 6 536 x lo‘6 'T' radians = NS T seconds of arc (107) T is the numerical value of torque in units of lb-in. This is the torsional deflection of each half of shaft. Each half is driven by a three inch section of one inch diameter tool steel shaft whose torsion adds to that of the shaft and is: 0 = “2;: E, = 2-54 x '0-4T radians (108) e g 0,525 T seconds of arc. The total torsional deflection is 9 2.: |,é75 'T _ seconds of arc. (109) This is about two times smaller than the allowable design limit. Furthermore, as the shaft is driven from the center, 133 torsional deflections should have the same sense and hence will subtract. The only possible net deflection would re- sult from different rolling properties of the two end bear- ings. Aside from torsional deflections we are also inter- ested in estimating the so-called critical speeds of the shaft. These are speeds of rotation at which resonances occur. For smooth operation it is desirable that the first critical speed (fundamental frequency of transverse vibra- tions) be at least twice the operational speed of 23 rps. Treating the shaft as a uniform solid shaft three inches in diameter with rigidly supported bearings, the first crit- ical speed is given by39 “=(L)Z(QEI V2 (110) I L [X 9 where L a distance between bearings (in inches) a gravitational acceleration (in./sec2) elastic modulus (p.s.i.) 2 moment of inertia (area), (in.4) (I cSr dA) 2) 5' H P! (Q I cross sectional area (in. density (lb/in3) S“ Numerically UO.’§ 292 radians/sec or f1'§ 46.5 cps. For the actual shaft, the stiffness to mass ratio is higher due to the taper and consequently its first critical speed is also higher. The fundamental frequency of transverse 134 vibrations for a finished shaft section supported by its ends is near 60 cps which is amply higher than the opera- tional frequency. (ii) The rotating shaft construction notes The shaft sections were made as follows: First, the rod stock was located between centers on a large lathe and the shape of the shaft was roughed out to within 1/8 of an inch of the desired diameter. A follow-rest and ade- quate cooling were used to prevent chattering and distor- tions. Very light cuts were then taken to reach the desired dimensions, with careful measurements taken frequently to check concentricity. This procedure yielded finished shaft sections that run true to within 0.002 inches along their entire length. The ends of the shaft sections were counter- bored to receive small diameter shaft sections that form connections to the driving pulley and the search coils. These smaller shafts were shrink fitted into the prepared holes. At the search coil ends the inserts are made of bronze, to prevent magnetic field distortions. The driven ends have the inserts made of tool steel. The search coils are held in position inside two inch diameter plastic holders, shown in Figure 31. Linen containing phenolic was used because of its machinability and superior retention of screw threads. Transverse holes were bored into the coil holders, forming a slip fit for the search coils. The coils are held in position by clos- ing these transverse holes by machined end caps, secured 135 'Figure 31. Cross-section of the spectrometer end of the rotating shaft. 135 Vito \\\ \\\\\~\;:;\:/:{B] \ finer - ‘1 “hilly/1.11172 47/1237/ [lull/fig? \x\\\\ ‘ \ A .. £40 \\ 137 by nylon screws. The leads from the search coils are brought down to the axis of the holders and soldered to a multi-pin male connector, which is glued to the bottom of a 3" deep axially slotted hole; bored into the body of the coil hold- ers. The holes are of slip fit dimensions for the bronze shaft inserts and are secured to them by tightening screws placed transverse to the slot, thus squeezing the plastic holder onto the shaft. A locating pin attached to the shaft ensures a prOper angular attitude of the search coil rela- tive to the shaft. The coil leads are brought from the connector at the tip of the shaft, through the center of the bronze shaft ends and then go out to the shaft surface through radial holes, after they have passed the end bear- ings. They are cemented to the body of the shaft by epoxy glue. The cable used for this purpose is shielded phono- graph pickup cable which has two twisted conductors encased in a braid shield. Its low mass and diameter and resistance to pickup of 60 cps hum were the reasons for its choice. Each half of the shaft has two cables cemented to it, di- ametrically opposite to each other, to maintain the dynamic balance of the shaft. One of these cables is a dummy, the other carries the coil generated signal to a pair of coin silver slip rings located near the driving pulley. The slip rings are press fitted onto a plastic sleeve and the coil leads are soldered to their edges. The signal is then picked off by metallized carbon brushes.‘ Three brushes ’Graphite Metallizing Corp., 1050 Nepperhan Ave., Yonkers, N.Y. 138 per slip ring are used to minimize noise. Figure 32 shows the central pulley assembly, showing the brush holders and the drive. The shaft is attached to the driving pulley through a flexible diaphragm joint which permits approximately 1/8 inch axial travel and is used to accommodate the thermal expansion of the shaft. The brass diaphragm of the flex- ible joint was taken from a discarded bellows steam pres- sure regulator. It is well suited for this purpose, for it is quite stiff to distortions in its plane, and yet its circular corrugations make it quite flexible for axial mo- tion. Near the center, the diaphragm is silver soldered to a brass collar which in turn is firmly attached to the steel extension of the shaft by six steel set screws, that are seated into matching indentations in the shaft. The outer perimeter of the diaphragm is attached to a recessed brass plate by 12 screws. The plate is fixed onto the ends of the driving pulley, by steel pins and screws. The weight of the shaft does not actually rest on the flexible joint but is carried by lubricant impregnated nylon sleeve bear— ings fitted to the inside bore of the driving pulley. No rotation takes place at these bearings. They serve only to bear the weight of the shaft and to allow axial motions of the shaft. The driving pulley is made of bronze. It is driven by five 0 rings that fit into grooves machined in it. 0 ring drive was chosen for its smoothness, for the tolerances 139 :.me ...uSiw 4m P5 400». .>w._.51 Zo_¢o ..(xhzuo m:# to ozfmam 204»: omkmn331 oz_>_¢o 20....0ww I mmoc 0 x03 03g 2¢81. 3 000w a: 700.1. 158 0.01% and has proved itself to be stable over long periods of time. 6.4 Performance After completion of the compensating coils, measure- ments were made in the vicinity of the mean orbit of the spectrometer to determine the magnitude of the residual fields. A saturable strip magnetometer‘ was used for these measurements. This instrument has a maximum sensitivity of 1 millioersted full scale.. Near zero field measurements can be made with a resolution of about 0.03 mOe. First, a position was chosen on the axis of the spectrometer and in its plane of symmetry. A jig was used to position the probes of the magnetometer parallel to the axes of the three pairs of compensating coils and the field was brought to zero for the three directions. Then, meas- urements were taken of the three field components at nine different positions: At the mean radius, at I 2 inches radially from it, in the plane Of symmetry, and 2 inches above and below the plane of symmetry of the machine. As could be expected, the uniform field of the compensating coils when added to the external field, which has a gradi- ent, produces a sine wave like residual field as the probe is moved around the spectrometer. A representative sample of such a measurement for the vertical component of the residual field is shown in Figure 36. The data collected ‘Magnaflux Corporation, Chicago, Illinois. 159 .omo...muomo. ...N+omo 2.9;. .mzja on N 6.5:. .2253 .2365. .mm manor. oovm .05 com. .09 now. com _ .00 con 90 «(Ill _ n- ”5.5.500 H. ---”... Nonfiom \\\\ # ...I. A w \_0. o o H, , _ \x I; . h I IL ... L .. ... L ..- _ _ 4‘ _ .\.O\ .Q/ / 1.; _ fl 1 4 \ Aw. _ x F .IIIIIIIIIIILI (I'lllllrlullllIIJ \s . r. I n e A. 4/ . .. e A _ \o \ _ / I, _ L . ex \ Q/ / L x \e _ ,/ ,. I I .- \ /O I . I |_r 4, I 30.3 _ ,. . _ m i /. q . 1 w . M ,7. L m _L L. I L I .. e I l. . T e , . e /. 2 A . ,, A. L 1 _ _ I“ . /.¢ 1 .I .I a / I / /e IIIIII. _ W W _ _ '1’! ¢./. _ H L x, 1“ __L--._I L- 160 from these measurements were used to calculate the amount of bias field needed to Obtain a zero net deviation for low energy electrons traveling along the mean orbit of the spectrometer. Note that a small residual field applied to the electron near the source may result in an appreci- able deflection by the time the electron reaches the counter. The calculation solves for a net field that has to be in- troduced, such that all the deflections will cancel. For simplicity the residual field is assumed to have a pure sinusoidal shape. It can therefore be written as __ l Bras. _ gresmnax COS 6 (11].) Considering a zero focusing field, this case can be resolved into a straight line of flight perturbed by Bres. according to ... = —Z—'\}" T;- . F ’4 r“) (112) A uniform biasing field 8b is to be added to Bres such that z - 0 at the end of the trajectory. In one dimension: m2. :-e'v- (B). + Bras.) (113) v is a constant velocity along the x-axis, B is directed along the y-axis. on e e I z + E— ’U' 85 + 7,;- ’V Brew”,< €059 -0 (114) I .As the 69 measurements start 30° away from maximum Br we must write 161 ’ .... _"E_ (115) cos 9 cos (6 + e. ) 6 now has range 0 to 7C {'2— radians. For an electron cl with momentum p - mv the time of flight is ’1‘: =7; where d :- 9T ERG. Time at position 8 is _6__:___J§2._62¢ mi: 0 7 1r 6 t9 =;T—;T’ = (116) The equation of motion becomes: 2 Z 2. 2’ 2 20 £20 :92 + P b + ,9 BFCSJMGX C0 with the boundary values: 4...}— at 9:: =0 d9 The solution is and 35.—.0 at 9:0. (118) Ia.1 z= SP Bream): [C05( 9 +15) + 931415. ~coslg]-(ll9) Condition for solution is z = 0 at 63-2-1112: _ 22.17)” gig. - '15th W — 0 —P— B i[Cos( {1+1 Q)+1TJ'2'$iM%-' COS‘J— 2T" 23sz (120) ab ‘ 0'163 Bres.max Bramaxz 2.3 mOe hence Bb 5“ 0.37 mOe (121) Similar calculations performed for the North-South field 162 and the East-West field yield Bb N-S cf 0.4 mOe (122) 8b a-w e 0.28 mOe (123) The current supplies were set at these bias field values at the center of the spectrometer. As the center of the spectrometer is inaccessible during operation, the refer- ence positions of the magnetometer probes were transferred to the outside of the tank. This is always possible to do, since the residual field passes through at least two zero field positions as one moves the probes around the circum- ference of the spectrometer, and so any value from zero to a few millioersteds can be obtained just by changing the positions of the probes. Three such external positions were determined for the three components of the field. During runs with the spectrometer, the field is compensated at convenient intervals, a few hours or so. Aside from drifts in the compensating power supplies, the variations in the earth's field are not very large, a few tenths of a millioersted in any given day. These are caused chiefly by causes beyond experimenter's control, such as parked cars in the neighboring parking lot, internal build- ing changes, magnetic storms and the like. To first order these disturbances (for the vertical field component) are ignorable, as the field control system of the spectrometer tends to compensate for them. CHAPTER 7 ALIGNMENT OF THE SPECTROMETER 7.1 Coil Measurements After completion of the focusing coils, careful measurements were made of the cross-section dimensions of each winding and thereby, of the mean radii of the coils. The measurements were carried out both at‘room temperature and near the anticipated operating temperature of the coils. The data were then used to compute the optimum spacing of the coils about the symmetry plane of the spectrometer. . In order to perform calculations of'an off-axis magnetic field produced by a number of circular coils it is necessary to determine the electrical equivalents of the coils, that is, the coils must be reduced to equivalent current filaments. Lyle30 has shown that a rectangular cross section winding can, in general, be reduced to two equivalent current filaments as follows. Referring to Fig- ure 37, Case 1. a :> b Coil is replaced by two filaments at radius E? r == EL -+ ( I 24 2") (124) Spaced a distance p above and below the median plane of the C011. 2' ‘- az - b: P - '2 (125) 163 164 V—“Rfl” l . l I l I R = MEAN RADIUS C1= AXIAL BREADTH b = RADIAL DEPTH FIGURE 37. DECOMPOSITION OF A RECTANGULAR CROSS - SECTION COIL INTO EQUIVALENT CURRENT FILAMENTS. 165 Case 2. b> a Coil is replaced by two filaments of radii r' 1 q lying in the median plane of the coil. 2. v.1: ( a (126) B ‘ + 2.4 21) ‘5.” = 52 _qz (127) 12. Table II shows the cold and hot a and b dimensions of the spectrometer coils. The A and B coils conform to Case 2 and the C and D coils to Case 1. The last figures of the radii in the table are not particularly significant, but were carried for purposes of computations and rounded off later. The equivalent radii were computed from these fig- ures as were also the values of p and q. Table III shows the results. All dimensions in Table III were converted to centimeters for future calculations. As the M.S.U. spectrometer is based on the Moussa- Bellicard design, using essentially the same design parameters, except for its larger size and low voltage, high current focusing coils, the Moussa parameters for 2 positions of the focusing coils were used as a departure point for sub- sequent more refined calculations. The axial positions of the coils are determined from: Z = Reg. E (128) where f has four different values for the four coil pairs. Particularly, SA =- 1.2, fa = 0.9, gc . 0.25, 'SD = 0.2. 166 TABLE II. Coil Winding Cross Sections W Coil a cold a hot b cold b hot Rm cold Rm hot Au 2.0000 2.0009 2.0605 2.0614 10.7618 10.7665 Bu 2.0000 2.0009 2.0758 2.0767 11.2694 11.2743 Cu 1.4000 1.4006 1.3360 1.3366 23.1810 23.1911 Du 1.4000 1.4006 1.3670 1.3676 19.7415 19.7500 A1 2.0000 2.0009 2.0665 2.0674 10.7618 10.7665 Bl 2.0000 2.0009 2.0745 2.0754 11.2688 11.2737 C1 1.4000 1.4006 1.3285 1.3291 23.1728 23.1828 D1 1.4000 1.4006 1.3787 1.3793 19.7526 19.7611 All dimensions in inches. TABLE III. Filaments for the Focusing Coils Equivalent Radii and the Spacing of Current C011 Req p q Au 27.3862 -—- 0.0364 Bfi 28.6742 --- 0.0408 Cu 58.9133 0.0307 --- Du 50.1751 0.0222 --- Al 27.3862 -—- 0.0382 81 28.6727 --— 0.0404 C1 58.8924 0.0324 --- Dl 50.2035 0.0179 --- All dimensions in centimeters. \“"_ I 167 This leads to the following axial positions of the coils (referred to the median plane of spectrometer): 2 cm 2 cm Au 32.8634 A1 32.8634 Bu 25.8068 81 25.8054 Cu 14.7283 C1 14.7231 Du 10.0350 D1 10.0407 It is clear that since the focusing coils sometimes depart significantly from the ideal equivalent radii, it would be valuable to calculate the magnetic field produced by the real coils and to optimize its shape by adjustment of their 2 positions. To this end we have first obtained the shape of a field varying as l/-JF} which incidentally gives a very good match for double focusing, and also the shape of the sixth order focusing field as found from the parame- ters calculated by Lee-Whiting and Taylor at Chalk River.20 Both were calculated to see how well they could be matched by positioning of the focusing coils and whether or not we had a choice. The sixth order field is, of course, by far the more desirable as it results in improved transmis- sion. Subsequent computations did show that the sixth order field could be matched quite well near the mean orbit of the spectrometer. Unfortunately the dimensions of the fo— cusing coils were such that a match better than 1 part in 104 was not possible for radial deviations greater than 2 cm on either side of the mean orbit. To find the field due to the focusing coils, one 168 needs to calculate the sum of the fields, off axis, of sixteen circular filaments spaced the apprOpriate distances from the plane of symmetry. For a single circular current we can write (referring to Figure 38): For A? ‘ —" _a- =41? ‘?--| ) B=VXA (129) r =[ L2 + fi’z -2L?Cose +zz]'/z =[(S’- Lcose)2' + (Ls‘me)2‘ + 2.11% 3’) £5§_ as (130) 471' [(9-Lco56)2’+(L sine): +zz]y2_ AI? =:/§2::=¢3 >1 “J2 I L casede o [(9‘ Lm5e)z+(L$ivI9)l + 221%; (131) let e= TC+24> ~ TCAIL , / A _I-I.LIJ (Z$‘“¢-I)d4> GIT + 2. 7. 4L? s'mzcb '/2. (132) . {[II. 9) +2 I[.- (ma-+22 }} “IL8> 2. Set (L'i' ?)z +22 h 52. Pktlk. [_ %Z shfd) ! A6 = 251' {-9-} J [(|- k‘sin‘OY/z- (I- k‘sin‘)/ ] (134) whence = Polk H; )V "___{ :1ij (|_ Siffl‘h _. M A 1,, old: ( ) _ _|_ __ 1S“:- ' _ . 135 kit-Jo" k 4’) d4) J00 _lk 5;“1¢)/2. } Recognizing the elliptic integral forms we have A6 :21: (9 VZHK --¥,—_-.E -K] or [”01 L VZ 2. ... I.) II.-%)K-EI Since + = +— _ : 3A9 ‘75. 3(?Ae) E3 ‘V'x,A\- S’ 3:2 -t §TET ‘9‘? Thus BF - — 9%? (137) and B = I _iU’Ae) , 3: 9 3? (138) Illlflll’EII’lll’lb} ‘Illlll 171 Finally, using the explicit value of k [‘01 .Z L + 9 I-le 8?: 2A [(L+?)2 zz]Vz(? _}[(:-9):+Z 2. E. K] (139) Iuol L 82’: Z'K[(L+?)z (“fl-I'll- [Tr—Ei' K] (140) The calculation is carried out in a straightforward manner using these expressions. Though simple it is quite tedious since it requires the evaluation of thirty-two ex- pressions to find the field at one point. Furthermore, the modulus of the elliptic integrals is not likely to be an even integer in most cases, requiring an interpolation in the tabulated values. It is altogether preferable to perform the entire calculation by a digital computer which can evaluate several field values per minute. 7.2 Computer Runs for the Optimization of the Focusing Field 8. T. Smith41 has prepared a MISTIC program for the computation of the magnetic field of a circular current. This program was used in all subsequent calculations. Several runs were made in the attempt to accomplish two main objectives: To match the spectrometer field to the sixth order field over as large a span of radius as possible, and to reduce the radial component of the field (Br) in the plane of symmetry. The radial field arises from the fact that the focusing coils are not perfectly 172 symmetrical pairs. The spacing of the focusing coils as calculated by Moussa, for example, assumes identical mem- bers of the coil pairs. If we have asymmetry, then the surface of zero radial field does not coincide with the geometrical median plane. For a pair of circular coils of slightly different radii and spaced distances -z and + (z + [3 z) from the median plane, the surface of zero radial field will cut the median plane in a circle whose radius is, of course, a function of the coil radii and 2 values. The objective here is to obtain Br . 0 on the mean orbit of the spectrometer, i.e., to make the locus of Br a O coincide with the mean orbit. To minimize Br analytically for a pair of coils of unequal radii and each containing two equivalent filaments is very tedious and, therefore, a numerical calculation was done by means of the computer to save time. Each of the coil pairs was placed initially at the Moussa setting and the radial (Br) and axial (82) fields were computed. The coils were then shifted in small increments relative to the median plane of the spectrometer and.Br and B2 were recomputed for several values of radius. The calculation leads to a choice of coil pair 2 positions Iwhich.minimize Br at the mean orbit of the spectrometer. ‘The results of these calculations are shown in Figures 39, 40 and 41. Examination of the figures reveals that the lkmussa indicated values of coil spacing do not give a zero radial field anywhere near the central orbit, though the actual adjustments needed to bring Br to zero there are 173 / , (R-Ro) BR 0 -l _ -2 -3 ‘O I 2 3 5 4 5 , (XIO M) ZPLS‘I'T-q- FIGURE 39. RADIAL FIELD OF THE B COIL PAIR As A FUNCTION OF ITS DISPLACEMENT RELATIVE To THE MEDIAN PLANE OF THE SPECTROMETER. 174 (IR-Re): +5 CM (R‘Ro)=-4 -I -2 O 5 IO Is 20 Z (XIO'5M) FIGURE 40. RADIAL FIELD OF THE C COIL PAIR As A FUNCTION OF ITS DISPLACEMENT RELATIVE TO THE MEDIAN PLANE OF THE SPECTROMETER. 1, /// (R-Ro)-420 a; // : // 5 IO I5 20 25 3O Z (x IO'5M) FIGURE 4|. RADIAL FIELD OF THE D COIL PAIR As A FUNCTION OF ITS DISPLACEMENT RELATIVE TO THE MEDIAN PLANE OF THE SPECTROMETER. 176 rather small. To obtain Br = 0 at ro the coil pairs had to be shifted as follows: a coils down 2.75 x 10"5 m C coils up 16.25 x 10"5 m D coils down 19.25 x 10"5 m Only the B, C and D coil pairs had to be treated. The A coils were symmetric and therefore had Br a 0 everywhere on the z a 0 plane. The D coils, aside from being nearest the central orbit, have the largest asymmetry. Consequently it is the D coil pair that determines the overall radial dependence of Br“ The value of the radial component of the field as a function of departure from mean radius is plotted for the B, C and D coils in Figure 42. It clearly shows the dominant character of the D coils. In this fig— ure the adjustments have already been carried out; there- fore, all three coil pair curves intersect at re. The total field is shown as a dashed curve. The slope of this curve arises from the asymmetries of the coils. Nothing, aside from rewinding of the coils, can be done to reduce it. Even so, for a I 2 cm departure from re, the radial field is about five orders of magnitude smaller than the axial field. The procedure for the optimization of the axial component of the magnetic field, 82, of the spectrometer consisted of two parts: First, the fields of individual coil pairs were calculated for different spacings grouped about the Moussa values. The results are given in Figures 43, 44, 4S and 46. The graphs depict the variation of the 177 (R’Ro) FIGURE 42. RADIAL FIELD As A FUNCTION OF RADIUS. .waadm m0 20:02:“— < m< Nm 2. ZO_.—.<_¢<> .0? “$307.— 178 SETS » m 0 ¢ n N . O _I NI MI QI DI 0.. .. n- «I _- Nm 0 de _ N 9.00 4 / n o\0NIuN< _ _ _ L r . _ _ a A _ o; .35: go 2962...: a 3 Nm 2. zo:. 41V wane; 179 .3 1m .. E n v n N . o ... N- n- v- n- o- .. ...: e. N... N- 1 III _ _ ox. _+ .u _ _ _ o ....I _ _ ~m< r _ N mIzoo m .\.«..u~< In L e _ _ (FIELIIIIII, --I III .II-IITIII,I#I I . 4-7.11.-- ; 1 fl _ _ _ . 180 .35: Lo 2952:“. < w< Nm 2. zo:<_m<> .9... Mano; so Calm: e n e n u _ o .. u- n- ..-, o- m- c- ”I NI O\0N+_II 1 _I .\._+ Nm 0 ~m< .\._II _ e\oNIuN< - N muzoo o n 1_ . «.2 x 181 .9454”. ....O 20:02:“. < w< Nm 2. 20:43.4) .®¢ mmDmu—m so Aomlmv m n v n N . o .- N- n- c- n- m- 'I n. “I .x. N... /III _- .x. _+ If _ _ _ _ _ _ _ . _ o Nm . _ _ _ “ ~m< 0\o_I IIIIIIIIIIIIIIIIIIII—WIIII— _II\I_IIII|IIIIIIIIII _ \\ O\O NIHNC .. III N IIIII m..:oo o_ n 1 1 1 . 0.x NI 182 axial field as a function of radius, (r - re). The spacing change (A z) is held as a parameter. The lepe and curvature of these curves provides a guide for the alteration of the coil spacing to improve the shape of the focusing field. The curves show that mo- tion of the C coils has the least effect on the total axial field, while the motion of the 8 pair produces the largest changes in the total field. Second, the influence of axial spacing of an indi- vidual coil pair on the total field was investigated. To evaluate the results of these calculations, the total axial field was subtracted from the sixth order ideal field, nor- malized at the central orbit radius. The differences thus obtained are plotted against radius, (r - r0). Figures 47, 48, 49 and 50 show the effect of moving the A, B, C and D coils in steps of A z a 1%. Clearly as all the curves have the same sense, it is impossible by any combination of coil motions to provide a perfect fit for a large span of .radius. The question that must be answered now is, there- fore, whether it is better to get a near perfect fit for small radial deviation and suffer a steeper departure from the ideal field farther out, or to try for a "good" fit (aver as large a span of radius as possible. The desirability of high resolution points to the first of the two choices. :Pt is preferable to have a near perfect fit in a limited region, for then the field shape improves as the machine is baffled down for high resolution running. 1‘33 .042."— ¢woco Ihxfi ..(mo. 20¢... 04w; J<_x< ...(PO... to ZO_P<_>mO .NV wN—Dmv—n. so “.mIm: m m. e n a . o _- a- n- c- o- o- n- N- I. :N _ T _- LIL III I |._ .l ..IIGMLI om _ _ _ _ Dame. 0 mmINm N- _ e \ _ _ E . IJ . I NI _ _ _ . 1 _ _- N 62.04%. 43:22 _ III 9:. . 2N .503 maupm 3 n 4.. 3 36: 3.3 < — A I F . a . ...? ¢ 4 e _ e A o; 184 .045... mwomo 1.52m ...(Mn: ICC... 049... 44354 JdkO... m0 ZO_._.<_>NO .mV HEDGE— 50 “cal m: o m. c n N . o _- - n- c- n- r ~+ ”I _+ I N- If x _ _ 3m: .33. .- I-_ / _ _ _ N- I . r _ a _ _ _ 6284.5 330.2 . - mi .:N :59. mambo. .\.. L6 36: 3.06 m . _ _ _ 185 .049... mwomo Ihxfi .._mO mV mm30.u 2o “calm: w n e n u . o .. - n- ..- a- v- n- IINI NI —.' /II _I .+ ~+ .\\-I-I/ ad... 0 mm V/ , ..«mo. wmINm _ m .ozGEm $302 ...... we.» ....N 503 $.um .+ n <.. .6 3.6: m...oo o _- NI __ ._ m . . .. 0.x 186 .OJwE Imam—O 1.52m -_wO .Om wm307¢ :0 Aoml m: m n c m N _ o .- N- n- ..- o- e- IIINI 1 n.- .. N- . —| m Illeulz o m 44mg. 0 N _ m.- — . N... N _ _+ 62.3...» «...-.322 2N n M...» ....N 584 mam»... .- .\.. E 36: 3.3 o N- e _ _ . . _ 0.x ”I 187 We should thus choose a curve that has an inflec- tion point at the mean radius and is most nearly flat in its vicinity. Study of the curves and the numerical data from the computer showed that one of the best curves was obtained when the D coils were moved in (toward the z - 0 plane) by one percent. This position was therefore taken as the second departure point for further computations. During the second phase of the calculations the radial component of the field was examined and corrected again, and the fitting to a sixth order field was repeated. The calculation did not yield an appreciable difference from the one percent shift of the D coils, or a significant improvement in the radial field. The final spacing of the median planes of the coils used in the final alignment of the spectrometer is shown in Table IV. TABLE IV. Axial Spacing of the Focusing Coils Coil pair Spacing from 2:0 plane (cm) Au 32.863 A1 32.863 Bu 25.807 B1 25.806 Cu 14.745 C1 14.707 Du ‘ 9.917 D 9.959 188 7.3 Alignment of the Spectrometer The focusing coils and the Spectrometer tank are mounted on three threaded mounting posts. (These can be seen in Figure 5, the photograph of the machine.) Prelim- inary to the alignment procedure the tank was leveled by use of a high sensitivity spirit level. Measurements were taken around the circumference of the tank mounting flange and the unavoidable undulations allowed for in the leveling process. Micrometer readings of the flange then established the position of the median plane of the instrument. Measurements previously performed on the focusing coils have established the dimensions of the windings, and thus the distances from the equivalent filaments represent- ing the coils could be transferred to the outside of the coils with a fair degree of precision. The cleaned edge of the outermost turn of copper was used as a measuring position. A little experimenting has shown that to align the (coils by fixing the distances between the mounts at three or'mere points around the circumference would be folly, as the mounts were somewhat wavy. .Any method of using shims of JOhannsen blocks also had to be rejected due to the varied Iiiameters of the coils and the inaccessibility of some of the measuring positions. The coils were finally aligned In! use of a precision cathetometer capable of 0.01 mm reso- lution. Some compromise had to be made in the number of positions by which the coils would be set. Finally three 189 positions were chosen as near as possible to the adjusting screws. Three complete adjustment runs were made for all eight coils. The entire procedure took about two weeks to complete. The coils were adjusted to the nearest 0.01 mm, so it is hoped that the overall setting error of the centers of the coils does not exceed 1 0.05 mm at the measuring positions. 7.4 Phasing of the Rotating Coils During manufacture of the rotating coil system, the search coils were mounted nearly at right angles to each other, since the field of the spectrometer is vertical and that of the permanent magnet is horizontal. To bring the output signals of the coils into exact opposition, a fine adjustment is possible by means of tilting the perma- nent magnet. This adjustment can be made while the shaft is running. The procedure for phasing the coils is as fol- lows. First, the magnetic field of the earth is compensated. Second, a stable current is sent through the focusing coils and the sum signal from the search coils is minimized by using the Dekavider. A better minimum can then be reached by the fine phase adjustment. This process is repeated while the sum signal is being amplified to a higher and higher level until the best minimum is reached for the max- imum gain of the error signal amplifiers. The error signal loop is then phased for this particular current through ‘the coils. The phaSe setting, unfortunately, is not unique for all current settings of the spectrometer. This seems 190 to be an inherent property of this type of a field measuring system. The inductances of the search coils, the capacitance to ground of the signal carrying cables and the load of the voltage divider form a LCR circuit. The phase of the signal changes with different positions of the divider wiper arm. Therefore slight adjustments of the mechanical phasing are necessary for different currents through the focusing coils. Fortunately, as can be shown by a simple calculation, below, a slight mechanical misphasing results in rather large changes in the phase of the sum signal. These changes are easily observable on an oscilloscope connected just after the de- modulator. The normal signal should look approximately as a full-wave rectified waveform. A small phase mismatch will cause the cusps of the wave to move apart until, for signals 90° apart, it will resemble a series of S shapes. Phasing by observation of this waveform can be done to within 5 x 10'5 radians. A reversible motor connected to the magnet tilt mechanism permits this adjustment to be done remotely from the control room. To examine the character of the error Signal, let the output of the Dekavider be ED=1A+AA)Sin1wt+) (141) and the output of the Spectrometer coilbe Es =Asin1wt+1t) = -—As'mu>t (142) ‘The error signal is the sum signal 191 m N 11 ED+E$ (143) Ea =(A+AAI Sin(00t +<1>) - Asinwt Ea =(Acosqa +AAC05—A) sin (.31: + +(A5h‘4’ +AASIII4>)CosL-at (144) Since (I) and AA are small, the first order terms in (I) and AA give: EC 2 AASU‘L out + A43 (.05 not (145) Thus for non-zero values of (I) , the mechanical phase mis- match, the amplitude A4> can become rapidly larger than A A and a large signal will appear 90° out of phase with the desired error signal. Since, however, the demodulator output is proportional to cos 6 , the electrical phase angle between the error and the reference signals, it will tend to discriminate against the A43 cos wt part of the error signal and the power supply will still regulate even if this signal is fairly large. Regulation will begin to deteriorate when the cosine signal starts to saturate the error Signal amplifiers, thus reducing their sensitivity to the error signal proper. Given pure sinewave signals and a perfect adjust- ment of the relative phases of the reference and error sig— nals, the field output of the supply will be independent 192 of small mechanical phase shifts. In a real system, how- ever, a small 69 always exists. Therefore, the output of the demodulator is slightly sensitive to the A4) cos wt part of Be. The contribution of this part either adds or subtracts from the real error signal depending on the sign of (I) , causing focusing field changes dependent on 4) . One would expect the magnetic field to change fairly rapidly for (I) large and very slowly in the region where (b is near zero. This behavior has been observed. CHAPTER 8 COUNTER WINDOW AND SOURCE PREPARATION 8.1 Counter Window Preparation The side window Geiger-Mueller counter used on the spectrometer requires windows in the shape of long rectangu- lar slits. The slits are milled in ”window plates” that are demountable to facilitate window changes during an ex- perimental run with the spectrometer. The dimensions of the windows vary according to the size of the source used in the spectrometer and the resolution required. As a rule, the width of the window is chosen to be the same as the width of the source. The range of sizes is approximately 0.25 to 4 mm wide by 15 to 30 mm long. The thickness of a counter window, measured in micrograms per square centi- meter, will vary according to the energy range of the elec- trons under observation from about 5 ug/cm2 for electron energies of a few kilovolts to several hundred ug/cm2 for energies greater than 0.1 Mev. The window thickness is chosen to have nearly 100% transmission fer the lowest an- ticipated electron energy. Usually, a choice is made by following the results of Lane and Zaffarano42 who treat electron transmission by thin films in some detail. The counter window is usually made of a thin organic film, and except for the very low energy electrons, is self 193 194 supporting under the 6 cm of mercury counter gas pressure. Only windows that are wider than 1 mm and thinner than about 15 ug/cm2 need additional support. This is usually provided by soft soldering a fine copper mesh‘ over the counter plate window slit. The mesh is electro-formed from copper foil and is available in several sizes from 50 to 1000 lines per inch. The maximum transmission for a mesh of 250 lines per inch is 70%. The material, copper about 0.001 inch thick, is opaque to electrons having energies up to 130 Kev. We have also successfully supported thin windows by soldering a loose grid of 0.001 inch or 0.002 inch stainless steel wire across the slit of the window. The technique of preparation of very thin windows 43 and Burford44 has been studied in some detail by Smith at Vanderbilt University. Their findings indicate that ' the thinnest windows can most reliably be made of collodion, non-flexible U.S.P. The second best material is Zapon. Success in the actual preparation of thin windows that are free of leaks depends to a large degree on the manual dex- terity and luck of the individual experimenter and it is the firm belief of the author that in this field of endeavor (experience is indeed the best teacher. Thus only a general outline of the preparation method is presented here. First, a solution of collodion in amyl acetate is ;prepared. This can be done in two ways. Either stock (ether ’Buckbee Myers Company, St. Paul, Minnesota. 19S solution) collodion is directly mixed with amyl acetate, or the collodion can be dried first and then dissolved. There is no conclusive evidence to show one way preferable to the other. The total volume of the prepared solution should be small, say 10 ml. or so, since once prepared the solution will age in the course of a few days, gradually deteriorating to the extent that thin windows can no longer be made. A few dozen drops of the solution are then placed on a weighed microscope Slide, dried, and reweighed, giving - the weight per drop. The films are made by allowing a drop of the solu- tion to spread on the surface of water. When the amyl ace- tate solvent evaporates, the film can be picked up by a wire frame as a double layer and transferred to the window plate. Usually, multiple layers are used for counter win- dows, the layers being oriented at different directions to :reduce possibility of window rupture by strains "frozen" .in the individual layers. Normally no special cementing procedure is used to attach the windows to the window plate. The films are laid down wet, in quick succession, and in drying seem to attach themselves to the plate quite effec- tively. The overall window thickness is estimated by know- ing the approximate area over which a single drop of solu- tion will spread and the weight per drop. Normally, room temperature tap water is used. How- if the hardness of the water is such that sediment ever 7 stains show on the finished window, one should use distilled 196 water since the sediment grains will cause rupture of the window as soon as gas pressure is applied to it. The sur- face of the water must be kept very clean, otherwise the solution will not spread properly resulting in very non— uniform layers. Such films are very susceptible to strains and besides that, non-uniform windows are undesirable. Aside from this, the chief hazards are dust in the atmo— sphere, excessive humidity and lack of patience. Although thin collodion windows are relatively easy to make, the author feels that there is another avenue of approach to the counter window problem which may give prom- 45’46’47’48 have prepared self ising results. Many workers supporting films of inorganic oxides, such as aluminum oxide, and of pure carbon. Results of these papers show that alum- inum oxide films can be prepared down to about 10-15 ug/cm2 and if the span of the film is small, can be expected to support counter gas pressure without additional reinforce- ment. Carbon films, which have the additional advantage of being electrically conducting, have been prepared in varying thicknesses down to 4 ug/cm2.49’50 So far no re- ports have been found in literature about use of such films as counter windows. 8. 2 Source Preparation For.the investigation of very low energy beta spectra the preparation of the source is of major concern since any noneuniformity of the source or its excessive thickness will cause distortions of the spectrum. Self absorption in the 197 source itself and backscattering caused by the source sup- port both contribute to these distortions. The requirement of a source support or substrate that would give low backscattering from the source is a difficult one, for it means essentially that only materials of low Z should be used. A further restriction is imposed by requiring that the material be electrically conducting to avoid charging of the source and the consequent energy shift of the observed spectrum. Light metals are, as a rule, not suitable by themselves as they will not form self supporting films in the thickness range that is necessary for low energy beta spectroscopic work, namely 5 to 50 ug/cmz. Organic films are very easy to prepare in this range of thickness but are non-conducting. They require a layer of metal to be evaporated or otherwise deposited on them before a source can be placed on them. Thus part of their initial advantage is lost in the process. Furthermore, they can withstand only moderate temperatures, such as may occur during vacuum evaporation, and tend to break easily. In spite of all these disadvantages, metallized organic films are the most widely used source backings, primarily due to ease of their preparation. The most common of these are films made of formvar with a few micrograms of aluminum evaporated on them. Their total thickness can be as low as 15-20 ug/cmz. Most of the sources used in the M.S.U. spectrometer are made on such backings. The most promising material for source backings would be carbon in the form 198 of self supporting foils. As reported in the preceding 2 have been made. Their section, films as thin as 4 ug/cm manufacture does, however, present some difficulties. These are being studied at present and it is hoped to use these films in the future. A survey of film making procedures can 51 and the reader is re- be found in a paper by Parker et a1. ferred there for description of the experimental techniques. The preparation of the source itself can be carried out in a variety of ways, the most important and widely used of which are: vacuum evaporation, electro-deposition and ion ejection methods. The use of the isotopic mass separator is becoming more common as more and more insti- tutions are gaining access to these machines. IsotOpe sep- arated sources are, by and large, of the highest obtainable quality in terms of thickness and uniformity of the active deposit. Source preparation on this project is done almost exclusively by the method of vacuum evaporation. A brief description of the equipment and techniques follows. (a) The evaporator For a project that concerns itself with a large variety of radioisotopes and where the purity of the sources under study is important, it is desirable to have some means of preparation of uncontaminated sources. An evaporator was therefore designed and built which is of very simple, almost primitive construction and very ineXpensive and there- fore disposable. A cross-sectional view of the evaporator, Figure 51, shows its essential features. A brass base plate BELL-JAR 2 1 SOURCE AND MASK / / V SUPPORT / / 1:? j 1 SOURCE RING r” : / I FILAMENT I 1 EVAPORATION MASK [ \ CURRENT LEAD RUBBER GROMMET \\\\k\\\ VACUUM SEAL “\ \ PLASTIC SLEEVE RUBBER GASKET l\ \ FIBER WASHER CURRENT LEAD VACUUM CONNECTION FIGURE 51. SOURCE EVAPORATOR. 200 forms the main platform. A half inch vacuum pipe is soldered to it. The pipe contains a small quantity of glass wool to trap radioactive materials coming from the evaporator. A sawed off large size teSt tube forms the bell-jar. Current leads are brought through the base plate, insulated from it by plastic spacers and sealed vacuum tight by small rubber grommets. Two threaded rods with nuts form the support for an evaporating mask which holds the source backing in its mount. The evaporator is evacuated by means of a small diffusion and a fore pump vacuum system. The pressure is monitored on a thermocouple vacuum gauge. Filament power is provided by a 20 ampere 220 volt variac coupled to a step-down transformer. The outputs available are 0-4.5 volts and 0-46.5 volts. (b) Preparation of source backings The organic film backings that are in common use on the spectrometer are made of formvar, by allowing a drOp of solution' of known mass per drop to spread on the sur- face of lukewarm water. The source holding rings are cov- ered by several double layers of this film, left to dry and then covered by a thin layer of vacuum evaporated alum- inum to make them conducting. The aluminum evaporation is carried out in a large evaporator, allowing the treatment 'The formvar solution is prepared by dissolving approximately 300 milligrams of formvar in 15 milliliters of ethylene dichloride and then adding 175 drops of methyl alcohol. 201 of about a dozen source rings at a time. (c) Preparation of thin sources The evaporator uses filaments in the shape of 1/8 inch wide ribbon. The filament material most commonly used is platinum, although for some materials, such as tin, tantalum is preferred. The filament is bent into a trough shape to allow a certain amount of "focusing" during evap- oration. The open side of the trough is then placed very close to the underside of the source defining mask, which serves also as a holder for the source ring and backing. The efficiency of the evaporator depends on the distance of the filament from the mask and the size of the slit in the mask. Normally the source making procedure is as fol- lows: A quantity of radioactive material is placed on the filament and left to dry if it is in the form of a solution. For some isotopes it may be necessary to dry the filament in an inert atmosphere to prevent the formation of non- volatile oxides. A series of evaporations is then carried out. The active material is deposited on aluminum foils. After each step of the multiple evaporation procedure the foils are counted. The results of such "differential evap- oration” yield a curve of evaporation rate versus current through the filament, and also determine the presence of inactive low boiling point contaminants that must be elim— inated from the actual source if it is to be kept thin. .After this procedure has been completed, the filament is cleaned by flashing it to a high temperature and then 202 reloaded. After drying, any present contaminants are first boiled off onto a blank foil. Next, the mask and source ring are inserted and the source is made. The final thick- ness of the source depends chiefly on the evaporator effi- ciency for that particular isotope and on the amount of material that is loaded onto the filament. Typically the efficiency runs from about one to ten percent. CHAPTER 9 PERFORMANCE OF THE SPECTROMETER THE CONVERSION ELECTRON SPECTRUM 0? CS - Ba 137 9.1 Igtgoduction Preliminary runs with the spectrometer gave us an indication that the focusing field shape was quite good, particularly near the mean orbit. Resolution for conver- sion electron lines, measured as the full width at half maximum of the lines, was near the theoretical value.13 Comparison with the Vanderbilt spectrometer showed that for any given baffle opening we could do better in resolution by approximately a factor of two to four. Most of the preliminary runs and all of the stabil- ity runs were done using the internal conversion electrons from Cs-Ba137, which has the advantage of long half-life ('N'30 years) and is obtainable carrier-free from Oak Ridge National Laboratory. Sources are easily prepared from this material by thermal evaporation in vacuo. To evaluate the high resolution capability of our .spectrometer, we decided to attempt to resolve the L and la subshell lines in the conversion spectrum of this isotope. This experiment does present a severe test of the machine, as the LI’ LII’ LIII lines are spaced only slightly more than 0.04 percent apart in momentum. 203 204 Shortly after the beginning of the experiment we 52 have recently published results found that Geiger et al. of just such a measurement. Their data were Obtained on the Chalk River 7( V2 spectrometer, using a momentum reso- lution of 0.02 percent. We, of course, could not better this resolution figure for any source of reasonable inten- sity (to do this the source width would have to be less than 0.1 mm). Nevertheless, we were still interested in comparing results and were anxious to find out how well we could do with a spectrometer whose total budget outlay was only 2-3 percent of the Canadian machine. The Chalk River group, by the way, did not report any M subshell re- sults, so we can claim some small measure of originality there. 9.2 The Convegsion Electron Spectrum of Cs-Ba137 A historical sketch of the internal conversion proc- ess is presented in the next chapter. The discussion here will be therefore restricted to the decay of C8137 and its daughter Baa-137‘“. The decay scheme is well known: I57 ;€+ 55C582 rsj=o-SI4 Mcv (95 Z.) 2'6“" 06616 1111111111111“ 205 The two beta-ray components have been studied by Peacock and Mitchell,53 Agnew,54 Langer and Moffat,55 56 and others. Aside from the energies and in- Yoshizawa, tensities indicated on the decay scheme diagram, the results indicate that the 514 Rev beta transition has a unique first forbidden shape, while the 1180 Kev transition has a non-unique second forbidden shape. The spins and parities of the levels in the Ba137m daughter nucleus are quite well established as 11/2 (-) for the excited state and 3/2 (+) for the ground state. The transition therefore involves a spin change of four and a parity change, indicating a gamma ray of predominantly M4 multipolarity. Past measurements of the K conversion co- efficient and of the K/EZL conversion line intensity ratio, summarized below in Table V, confirm the transition as an .M4, but leave open the question of possible admixture of ES. To resolve this question, we need data regarding the relative intensities of the LI, LII and LIII conversion lines. The LI/LII and the LI/LIII intensity ratios provide a sensitive test of the multipolarity of the transition. 52 So far, only Geiger et a1. and the present work provide any measurements of the barium L subshell intensity ratios. The Canadian results and theoretical values obtained from Rose's73 and Sliv and Band's74 tables are shown in Table VI. Note that the experimental results are consistently higher than the theoretical values. The K/ 2'; L, LI/LII and LI/LIII will hence be below Rose's and Sliv4s values. Geiger notes 206 TABLE V. The K Conversion Coefficients and the K/ 2 L Line Intensity Ratios for Ba137m K K/ 2 L Reference 0.081 ---- 57 0.118 ----- 58 0.097 1 0.003 59 0.095 t 0.005 — — — 60 0.11 I 0.01 6.0 I 0.1 61 0.096 I 0.005 4.6 I 0.2 62 0.092 1 0.006 5.8 I 0.3 63 0.095 I 0.008 — _ _ 64 0.093 I 0.018 -— 65 0.0976 1 0.0055 5.66 I 0.04 56 0.093 1 0.006 — 66 0.093 I 0.005 —= — 67 ___—— 5.5 --- 68 -__ 4- - 5.43 I 0.05 69 __ 5.2 I 0.2 70 — 5.9 I 0.1 71 0.0918 5.66 (Rose, point7gucleus) 0.094 ' 5.58 (Rose, finitganuc.) 0.093 5.38 (Sliv) 74 207 TABLE VI. Relative Conversion Line Intensities W Line Geiger Rose (M4) Sliv (M4) x 1 I 0.02 1 l 5:L 0.192 I 0.006 0.179 0.186 l.I 0.151 I 0.004 0.143 0.148 LII 0.0222 1 0.0011 0.0202 0.0207 LIII 0.0189 1 0.0010 0.0165 0.0171 this discrepancy and suggests about three percent admixture of ES to bring the data into agreement. At the same time, however, he argues that such admixture is not very likely, since it would require an enhancement of the ES component over the single particle rate (by about a factor of 50). He does not present any other explanation but mentions that presence of systematic errors could not be excluded. Our .results, except for the K/2;L ratio which falls very near the predicted value for pure M4 radiation, confirm Geiger's .results. Our errors, however, are considerably larger due to poorer resolution and statistics. 9 . 3 The ExEriment (a) Source PreparatiOn The source was prepared by evaporation in vacuo. anus evaporator filament was first thoroughly cleaned by flashing it repeatedly to yellow color for 5-10 second in- tervals. After cleaning, the filament was loaded with about 208 137 (obtained two drops of stock solution of carrier free Cs as CsCl in 1 N HCl from Oak Ridge National Laboratory) and dried with a heat lamp. A differential evaporation proced- ure was then carried out (see section 8.2, (c)) to deter— mine low boiling point contaminants. The preliminaries completed, the filament was cleaned again, reloaded, contaminants boiled off. The source back- ing (15 ug/cm2 aluminized formvar film) and the source de- fining mask were placed in the evaporator and an evapora- tion was carried out. Due to the small size of the source defining slit, 0.25 mm x 15 mm, a total of fourteen evap- orations had to be done onto a single source backing to obtain a source of usable intensity. Immediately after preparation, the source was barely visible to the naked eye. In the spectrometer no thickness effects could be 137 K conversion line. The resolution ob- seen on the Ba tained with this source was 0.047 percent (full width at half maximum). (b) Data Collection Several passes were made over the entire conversion spectrum, running both upward and downward in momentum. The spacing between successive points was 25 on the dekavider, corresponding to 25/403000 or 0.0062 percent in momentum on the K line. On the average, seven three- minute counts were taken at each point. .About a dozen runs were made over the L and the M lines. During the data run, which for the most part was 209 conducted on a 24 hour day basis, background and earth's field compensation readings were taken about once every eight hours. Usually one ten minute background count was taken and the shut-down time of the spectrometer used to reset the compensating field back to zero. In addition, to keep track of the spectrometer drifts, a preselected point on the upper sideband of the K conversion line (called by us the ”calibration point") was checked for three 3-minute counts once every two hours. (c) Data Analysis The first step in the treatment of the raw data was the subtraction of the background and the application of drift corrections. The background and the reference point counts were plotted against time, the graphs smoothed out somewhat and the corrections then read off to the near- est integral count, directly from the plots. It should be made clear at this point that the counts taken at the calibration point yield a very sensitive measure of the focusing field drift. In fact, the lepe of the upper side- Iband of the K conversion line is so steep in this case that -a change of one part in 105 in the field is easily detected -as a counting rate shift of some ten percent (for a point lualfway up the peak). The drifts were corrected to the nearest 5 units :in.the last dekavider place. All the run data were then collected together and all points were averaged around dekavider settings spaced by 25 units. The plot, Figure 52, 210 . Mm I m0 .wO mmflfifi COHMFH®>COO HMCCHQPCH .Nm QCHSWHE Eema ema 0009‘? on" 0009? a fi SON? .Y . .4..- \.\. . O ..s .... O O f.\’ p........ x... *0 00 3.1.... .... 04... .... 0.2 ...... ...... o .../...... o 1 00.0 ... 3x \\\_ \__/_ / .003 .x .... n: .x .r mx .83 _ _ _ .. .. ... i 3.0 3.580 3.43 ...... 3.0.5.0 9.0.9..th 32.00 R 30.0 car): zonauoeum $2. ZO_mdw>z d m .000 211 represents these three minute averages divided by the dekavider setting to make the data suitable for relative intensity measurements. The shape of the K conversion line was assumed as a standard for fitting the L and M subshell data. The LI, L and LI II II M group we could fit only MI, MII III and MIv V' From Fig- , 9 lines could be fitted unambiguously. In the ure 52 it can be seen that the second and third, and the fourth and fifth lines of the M shell are far too closely spaced to be resolved. We did, however, manage to separate the N+0 shells from the M shell electrons. The fitting is shown in Figure 52 by dotted lines. The errors in the present data are shown in the next section and are primarily due to statistics. They represent the latitude with which the individual lines may be fitted, while their sum remains within the probable error of the experimental points. It is also possible that the data contain systematic errors unknown to the experimenters. 9.4 Results and Conclusions The results of this experiment are shown in Figure 53 and in Table VII. The figure shows theoretical values of the conversion line intensity ratios, plotted against the energy of the transition. Both Rose's and Sliv's values are presented. The experimental values of Geiger et al. and of the present work are also indicated on the graph. Table VII summarizes the above information and adds our results for the M shell. It can be seen that our results 212 .>o¢wzu 20..—._mz<¢._. ...O ZO_POZD..._ 4 m4 moi-(m rtmzmkz. NZ: zo_mmw>zoo .00 memv—L .Nox ...o 3.2: 2.. Smmzm o. 6.. .... N.. o.. no . c \\\\h-\\ n IIIIIIIIII 1In.1Il-..- II #— -\l_.\\ w . \I\ ..w? II -II4 .. w I I. III\\ 1 a 1.. xmoz ..zmmumal I 6 No.2... =I—\_l_ 1 .JdFM two—U0 O. >tmzwhz. .1 2.5 IIII 1 .\ \\_ mmom -\\\ ...-<3 18 11 225 20:454.. 4.... _ 213 137m TABLE VII. Relative Intensities of Ba Conversion Lines Theory Experiment Line Rose Sliv Geiger Present work x 1 l l I 0.02 1 1 0.04 1(a) ----— ----- — 0.182 I 0.010 (b) + ... 211. 0.179 0.186 0.192 - 0.006 0.178 - 0.010 LI 0.143 0.148 0.151 1 0.004 0.140 I 0.007 LII 0.0202 0.0207 0.0222 1 0.0011 0.0207 I 0.0046 1.III 0.0165 0.0171 0.0189 1 0.0010 0.0171 1 0.0041 M(a) ---- ----- - ————— 0.0411 1 0.0037 MI 0.0565- ---- = — __- _ 0.0233 3 0.0030 M11 111 0.0200- ----- 0.0145 1 0.0020 7 HIV v 0.0002: ------------------ 0.0047 1 0.0016 9 N + 0 ------------------------ 0.0095 1 0.0031 K/L ---------- = — _-=_ '5.51 I 0.36 K/ZL 5.58 5.38 5.21 2‘- 0.16 5.63 I 0.38 LI/LII 7.07 7.16 6.80 I 0.38 6.75 i 0.55 T + 'The theoretical values of the M line intensities were ob- tained by extrapolation from Z-GS and higher. (a) (b) Sum of the areas of the fitted lines. Area under the experimental points for the entire shell. 214 are in fairly good agreement with those of Geiger, partic- ularly in the case of the L subshell intensity ratios. In our case, the K/L ratio and the relative inten- sities of the LI, LII and LIII lines are closer to the the- oretically predicted values for pure M4 radiation. Geiger's values, on the other hand, are consistently high. We cannot draw any definite conclusions from this, however, as our results contain substantially larger errors and a glance at Table VII shows that there is a considerable amount of overlap in the results of the two experiments. I feel that the agreement in the LI/LII and LI/LIII ratios gives us a greater degree of confidence in saying that a small amount of BS admixture exists in this decay. We have to qualify this conclusion, however, that it still may not be so in case that both Chalk River and M.S.U. ex- periments suffer from similar systematic errors. Perhaps the experiment ought to be done on a high resolution machine of different type, such as the uniform field solenoidal spectrometer of Jungerman.14 The M shell results are new. Unfortunately the relative line intensities cannot be readily compared with theory, as Rose73 calculates the M shell and subshell con- 'version coefficients only for unscreened point nucleus. The theoretical values of the conversion coefficients are therefore likely to.be high. Only the total M shell con— version coefficient is available near the desired 2 - 56 'value. The M subshell coefficients must be obtained by 215 extrapolation, since the tabulation covers only 2 2> 65, with 152 a 5. Such extrapolation has been carried out. The errors in the individual M subshell coefficients may be high, but the general agreement of the total M conver- sion coefficient with the sum of the extrapolated values indicates that it should be less than a factor of two for the MI line and possibly also the ”11,111 line. The MIV,V line is much more uncertain, perhaps as much as an order of magnitude. Looking at Table VII, it is clear that the theoret- ical line intensities do not agree with experimental results. It should be noted, however, that the experimental values obtained for the M, MI and the "11,111 lines are consistently low by roughly a factor of two. The drastic disagreement in the MIV,V line can be easily accounted for by assuming a greater overlap of this line with the conversion line group arising from the N + 0 shells. In this work the group was separated only by an empirical guess--the statistics in this region are very poor. These results are generally in agreement with the M subshell relative line intensities obtained by BackstrSm, Bergman and Burde7S for the 50 Kev (M1) and the 158 Kev (52) transitions in Hg199. The L/M ratios are quite similar: Multipolarity L/M (theory) L/M (exper.) 39199 so Kev m 1 2.11 3.97 39199 158 Kev E 2 2.06 3.85 Ba137m 662 Kev M 4 2.40 4.43 216 In conclusion, it should be said that the spec- trometer drifts proved to be sufficiently smooth that they could be well accounted for by the calibration point checks. At the present time, therefore, there is every reason to believe that with a sufficiently narrow and intense source, the spectrometer resolution could be brought down to the 0.01 percent level. CHAPTER 10 THE CONVERSION ELECTRON SPECTRUM OF RADIUM D 10.1 Introduction A nucleus may decay from an excited state by the emission of electromagnetic radiation (gamma rays) or by a radiationless transition wherein the transition energy is transferred to one of the extranuclear electrons, eject- ing it from the atom. This process is called internal con- version, the ejected electrons being the internal conver- sion electrons, or more simply but less precisely--conver- sion electrons. It is this electromagnetic interaction between the nucleus and its atomic electrons that allows zero angular momentum change nuclear transitions to proceed, although such transitions are strictly forbidden by the selection rules governing the emission of electromagnetic radiation. As internal conversion and gamma ray emission are, in the majority of cases, competing processes, it is use- ful to define an internal conversion coefficient as the ratio of the number of electrons to the number of gamma quanta emitted per unit time for a given transition. The usefulness of the internal conversion coefficient stems from its dependence on the transition energy, the nuclear charge Z, the angular momentum change and the parity change 217 218 involved in the transition. The usefulness is further aug- mented by the coefficient's insensitivity to nuclear struc- ture. In the history of our understanding of the internal 76 77 conversion process, Ellis and Meitner were the first investigators to give an empirically correct interpretation of the ”line spectrum” of beta rays. Taylor and Mott78 were the first to point out that the internal conversion process cannot be accounted for by photoelectric effect mechanisms, but has to be considered as a direct coupling of the electrons with the electromagnetic field of the 78 and Hulme79 also performed nucleus. Taylor and Mott some of the earliest reasonably precise calculations of the internal conversion coefficients. The interim years since the nineteen thirties have seen the full development of the theory with the inclusion of complete relativistic treatment of the process, magnetic and screening effects80 and finally allowances for finite nuclear size.81 In the post war years several sets of calculations based on approximate models were made, such as that of 107 Gellman, et al., for example, who used a point nucleus and relativistic unscreened electrons. The first extensive set of tables was published by Rose, et al.,82 in 1951. In these calculations the nucleus is still assumed to be (a point and therefore no details of nuclear structure enter into these computations. The nucleus is assumed to be screened by the atomic electrons. As Rose pointed out 219 later,72 such calculations lead to virtually exact results. Nuclear size, however, was found to play a more important part than originally thought. The point nucleus coeffici- ents were found to be high by some 30-40 percent, particu- larly for the higher 2 elements and for magnetic transitions. Calculations of conversion coefficients with the finite size of the nucleus taken into account were first 81 published by Sliv and Band for a limited number of Z values and energies. Subsequently, extensive tables were prepared both by Sliv and Band74 and by Rose.73 The dif- ference between these two compilations concerns the finite nucleus corrections. Sliv and Band use a special nuclear model which assumes that all nuclear currents flow on the surface of the nucleus. Rose, on the other hand, corrects the electron wave functions for finite nuclear size. The difference between the two sets of tables is approximately ten percent. Finite nuclear size effects lower the values of the conversion coefficients as compared to the point nucleus calculations, especially for magnetic multipole transitions and in the region of heavy elements. A further refinement, a method for correcting the calculations to take account of different nuclear models, has been worked out by Green and Rose.83 The validity of the finite nuclear size assumption and the nuclear structure corrections are supported by ex- perimental evidence of Wapstra and Nijgh,84 McGowan and 85 86 87 Stelson, Nordling, et al., Church and Weneser and 220 others. The dependence of the internal conversion coeffi- cients on the assumed nuclear model is a mixed blessing, for although it allows new information to be gained concern- ing the nuclear levels involved in a transition, the con- version coefficients are no longer as perfectly clear cut a tool for the determination of the multipolarities of the competing gamma radiations as was originally thought. Never- theless, this does not destroy the value of the coefficients, for their sensitivity to nuclear structure is low, of the order of a few percent, whereas their variation with energy, multipolarity of the transition and the 2 value is quite large.88 10.2 The Decay of Radium D The history of investigations concerning the decay of Ra D presents a rather curious picture. From its dis- covery at the turn of the twentieth century until 1939 its decay was thought to be a simple beta-ray decay followed by a single gamma ray. Then in subsequent years the decay scheme gradually grew in complexity, reaching a peak in 1949 when seven distinct gamma rays were thought to be present. After this time the number of gamma rays attrib- uted to radium D began to diminish as more carefully per- formed experiments and improvements in the experimental technique identified many of them as spurious (for example: fluorescent X-rays from the walls of the counters used). .At present we are essentially back to the simple decay of 221 the nineteen thirties, with the exception of having two beta transitions instead of the original one. The contem- porary decay scheme is: 0+ sz'o (RaD) (3— l7 Kev 85 % 46.5 Kev 64 Km ’f ‘_ 4 Biz“) (ROE) The low energy of the predominant beta ray presents a rather difficult measurement problem. The first defini- tive measurements were done by Richardson and Leigh-Smith89 who give two possible values for its end point energy: 16 Kev by fitting the spectrum to Fermi's shape predictions, assuming a (0,0) transition, or 24 Kev by assuming a (0,1) transition and fitting the shape to Konopinsky's shape pre- dictions. Lee and Libby90 used magnetic deflection methods and obtained 25.5 I l Kev for the end point energy of the 91 92 in 1950 beta spectrum. Kinsey in 1948 and Cranberg suggested that there may be branching in the beta decay, and estimated the two components to have end point energies of 15 Kev and 60 Kev. Considering that at that time the 64 Kev beta ray had not been observed yet, the prediction 222 was remarkably good. Insch, Balfour and Curran93 measured the end point energy of the low energy beta spectrum as 18 3 2.5 Kev and determined the disintegration energy of radium D as 64.5 1 2.5 Kev, using a proportional counter. Their analysis identifies the 18 Kev beta ray emission as allowed, unfavored, with log ft value of 5.5. They assume the 64.5 Kev beta transition to the ground state of B1210 to be absent, saying that if it exists at all, it will have low intensity. Jaffe and Cohen94 offer the first tentative experi- mental evidence of branching of the beta decay. Their re- sults show the low energy beta ray end point to be 16.7 I l Kev. They conclude that at least ten percent of the de- cays proceed by a 55.6 Kev end point beta transition to a 7.8 Kev level of 81210. In a later paper,95 however, they 210 does not really ex- report that the 7.8 Kev state of Bi ist, the "gamma ray" being actually a fluorescent X-ray of copper excited in the walls of the counter. Their final conclusion is that the evidence for the existence of a higher energy beta ray was inconclusive. The same year (1953) Wu, et al.,96 suggest, still tentatively, that on the basis of measurements of the number of unconverted 46.5 Kev gamma rays per disintegration of the parent RaD, there may be 8 3 5 percent beta transitions proceeding to the ground state of 81210. The first definitive evidence of the existence of the higher energy component of the beta decay and a 223 measurement of its intensity were obtained by Stanners and R05597 in 1956, using electron sensitive emulsions impreg- nated with citrate of radium D. Their results show the 64 Kev component to have an intensity of 15.5 t 3.5 percent. 98 obtained a In a later measurement Tousset and Moussa branching of 19 I 4% and 81 I 4% for the high and low en- ergy components respectively. The values accepted at the present time by the com- pilers of nuclear data tables are 15 3 4% for the 64 Kev component and 85 1 4% for the 17 Kev component of the beta decay. The study of the gamma rays following the decay of RaD presents an even more varied and interesting pic- ture: Early investigators, between the years of 1912 and 1935, essentially agreed on the existence of one gamma ray of approximate energy of 47 Kev.90 99 In 1939, however, Amaldi and Rasetti reported an additional weak gamma ray with energy of 43 Kev. This experiment was repeated and expanded 100 after the war in 1945 by Tsien who reported six gamma 101 like- rays. A crystal diffraction experiment by Prilley wise gave six gamma rays and suggested a seventh at 65 Kev. The energies, as reported by Tsien, were 46.7, 43, 37, 32, 102 in 23.2 and 7.3 Kev. A later study by Cork, et al., which the gamma ray spectrum was studied via the observa- tion of conversion electrons, is in direct conflict with the results of Tsien and Frilley, for it reports that there is no evidence of gamma rays other than the 47 Kev one. 224 The authors feel that any other gamma ray with intensity as low as one percent of the 47 Kev one would have been 103 while detected. On the other hand, Butt and Brodie, performing a similar experiment using a lens beta-ray spec- trometer, conclude that at most 70 percent of the decays proceed via the 46.7 Kev transition. They suggest the ex- istence of four other gamma rays having energies of 31.3, 104 point 23.2, 16.1 and 7.3 Kev. In 1953 Damon and Edwards out that, aside from the 46.5 Kev gamma ray, only one other could be found that gives rise to a weak conversion line and that conversion electrons from the other gamma rays have never been observed. Their measurements, using a brass prOportional counter, verify the existence of the gamma rays reported by Tsien, except for the 7.8 Kev one which they suggest to be due to X-rays of copper in the walls of the counter. The gamma rays (and their intensi- ties per hundred disintegrations) thought to be in existence at this time are: 46.7 3 0.1 Kev 3.5 + 0.4 % 41.5 3 l ’ Kev 0.1 % 37.0 3 0.5 Kev 0.1 % 30.7 3 0.5 Kev 0.4 % 24 3 0.5 Kev 0.3 or less % 16.1 3 0.3 Kev 0.5 % An extensive systematic study of the RaD gamma ray spectrum was undertaken in the same year (1953) by Wu, Boehm and Nagel.96 They showed the 7.3 3 0.7 Kev line to be due to copper or nickel fluorescence radiation, by performing experiments with proportional counters made wholly of brass 225 and aluminum, and by backing the source with a copper sheet while using an all aluminum counter. The 7.3 Kev line ap- peared whenever copper or nickel were near the source, and was absent when the experiment was performed with an alum- inum counter. The 23 Kev gamma line was identified as a pile-up effect of the L x-rays of BiZIO. If the propor- tional counter registers two L X-rays as a single sum pulse the energy would be in the correct range, i.e., the sums Lo, + Lo, , L0( + L“, and L9 + Ls give energies in the range 22 to 26 Kev. The 16.1 Kev line is tentatively identified by Wu as the LT x-ray line of Bi. The remain- ing lines, the 42.6, 37 and 31 Kev gamma rays were not re- solved in this experiment due to their close proximity to the 46.5 Kev line and its escape peak at 34.2 Kev. From conversion electron studies, however, they place an upper limit on the intensity of all three of these lines as less than 0.5 percent. Thus Wu, et al., conclude that the 46.5 Kev line is the only gamma ray of significant intensity present in the decay of RaD, a conclusion which is also supported by the lack of conclusive evidence for the pres- ence of conversion electrons for any of the other gamma transitions. 105 Subsequent work by Damon and Edwards confirms the findings of Wu,-et al., and a very carefully done ex- periment with freshly chromatographically separated carrier 106 free sources of RaD by Pink, et al., shows that if other gamma rays exist their combined intensity would have to be 226 less than 0.2 percent of the 46.5 Kev photons. The story has, therefore, come a full circle and the decay of RaD may once again be regarded to be simple. 10.3 The Conversion Electrons of Radium D The first post-war investigator of the conversion 92 who used a 180 electron spectrum of RaD was Cranberg, degree spectrograph with calibrated electron sensitive emulsions. In his spectrum he does not resolve any of the subshell lines of the M, N and O shells and has some difficulty resolving the lines of the L shell. He measures the number of decays accompanied by L shell conversion as 54 percent. Using a value of 3.5 percent for the number of unconverted gamma rays, he obtains for the L shell con- version coefficient a value of 15.5. Cranberg also presents in this paper a brief summary of previous work dating from 1912 to 1926. A summary of the results of this and other papers discussed in this section is presented in Table VIII at the end of the section. 103 examined the conversion electrons Butt and Brodie from RaD by a lens spectrometer. Their resolution, however, was very poor. No L subshell structure is apparent in their spectrum, nor do they resolve the M, N, O shells. From their data they find 46.7 3 4 percent of the decays accom- panied by L shell conversion, leading to the conversion coefficient value of 13.5. Their discussion leading to 227 the assignment of spins and parities to the various levels involved in the decay is rather interesting (though wrong). They suggest that since RaD and RaF are both even-even nuclei, with ground,state spins 0(+), that the ground state of RaE ought to be 2(+) on the basis of Gamow-Teller selec- tion rules, taking the RaE beta spectrum as second forbidden beta decay. They assign l(+) to the excited state of RaE, which gives the 46.5 Kev gamma ray a A1 = 1 and AK , no, suggesting that Ml radiation should be in even compe- tition with 82. Experimentally, though, they agree that the conversion coefficient 0HHnmmm 33 mumncmuu ucmmmum. Add me” mpH mum rimmI can (mos mime .IHMO oucmummwm m.mH «.ms m.ma u: :u m.ma u: ”.6 m.mH .wwwwow m.oum.a u: s: s: ~.ue.a ¢.a m.H N.HH.~ m.na. R.HH.N Ho nuunuuu u- u: nu HH>.H>z unusunu nu I: u: m.um.m m 5.6 H.nm.m Huh Hum.m >Hz mo.onma.o nu nu :: HHHz HH.oumm.o u- u: u: HHz mm.ouhm.m us I: nu t 4 4 : Hz IIIIIII I: I: 3803 W >2 IIIIIIn I: II A x003 fl «.mm. >Hz mm.oum~.o nu us m.m~ m.nm.mm em m.o mnem # Numm HHHz m.onm.w n: :: ~.m Numm Ha: s.onm.- u. an e.m~ H H: m~.nvm. u. u: ~.nm.o m.o o.a mo.nmm. m.ua. w.ona.a HHHA e.oua.aa -u u: m.ue.m m.m m.oH mums m.nm.p m.~uo.m HHA «.muOOH s: In can can con ooa ooa ooa cos Ha hudmcwucH m>wumHom mafia sumo cowuumam coauwm>dou mom mo humeesm .HHH> mam<9 232 by evaporating the lead very slowly, over a period of min- utes, and at very low temperature. The source dimensions were 1 mm x 25 mm. The source was sufficiently thin to show no appreciable thickness ef- fects down to approximately 7 Kev. The resolution, full width at half maximum, on the LI conversion line is 0.18 percent. (b) Data Collection Approximately eight passes were made over the en- tire conversion spectrum of RaD, running both upward and downward in momentum. The data were collected in essen- 137 experiment tially the same way as in the case of the Cs described in the previous chapter. The upper sideband of the LI conversion line was used as a calibration reference point. (c) Data Analysis The data were corrected for background and for spectrometer drifts in much the same way as described in section 9.3(c).‘ The lower resolution used in thisexperi- ment makes most of the drifts negligible in comparison to the line width. Figure 54 shows the final form of the data. All the runs were averaged and the points represent counts per minute divided by the potentiometer setting. ‘Fairly frequent background readings were taken. The source material tended to contaminate the spectrometer ‘vacuum tank gradually raising the background level. .Qmm mo Edepoomm compomao coemeo>coo era .rm mesmflm go Q